You get these trophies by beating Classic, Adventure and All-Star Mode with each character:
001. Mario
002. Mario (Smash 1)
003. Mario (Smash 2)
004. Donkey Kong
005. Donkey Kong (Smash 1)
006. Donkey Kong (Smash 2)
007. Link
008. Link (Smash 1)
009. Link (Smash 2)
010. Samus Aran
011. Samus Aran (Smash 1)
012. Samus Aran (Smash 2)
013. Yoshi
014. Yoshi (Smash 1)
015. Yoshi (Smash 2)
016. Kirby
017. Kirby (Smash 1)
018. Kirby (Smash 2)
019. Fox McCloud
020. Fox McCloud (Smash 1)
021. Fox McCloud (Smash 2)
022. Pikachu
023. Pikachu (Smash 1)
024. Pikachu (Smash 2)
025. Ness
026. Ness (Smash 1)
027. Ness (Smash 2)
028. Captain Falcon
029. Captain Falcon (Smash 1)
030. Captain Falcon (Smash 2)
031. Bowser
032. Bowser (Smash 1)
033. Bowser (Smash 2)
034. Peach
035. Peach (Smash 1)
036. Peach (Smash 2)
037. Ice Climbers
038. Ice Climbers (Smash 1)
039. Ice Climbers (Smash 2)
040. Zelda
041. Zelda (Smash 1)
042. Zelda (Smash 2)
043. Sheik
044. Sheik (Smash 1)
045. Sheik (Smash 2)
046. Luigi
047. Luigi (Smash 1)
048. Luigi (Smash 2)
049. Jigglypuff
050. Jigglypuff (Smash 1)
051. Jigglypuff (Smash 2)
052. Mewtwo
053. Mewtwo (Smash 1)
054. Mewtwo (Smash 2)
055. Marth
056. Marth (Smash 1)
057. Marth (Smash 2)
058. Mr. Game & Watch
059. Mr. Game & Watch (Smash 1)
060. Mr. Game & Watch (Smash 2)
061. Dr. Mario
062. Dr. Mario (Smash 1)
063. Dr. Mario (Smash 2)
064. Ganondorf
065. Ganondorf (Smash 1)
066. Ganondorf (Smash 2)
067. Falco Lombardi
068. Falco Lombardi (Smash 1)
069. Falco Lombardi (Smash 2)
070. Young Link
071. Young Link (Smash 1)
072. Young Link (Smash 2)
073. Pichu
074. Pichu (Smash 1)
075. Pichu (Smash 2)
076. Roy
077. Roy (Smash 1)
078. Roy (Smash 2)

     You get these by doing certain things in 1-P Mode:
082. Giga Bowser - Defeat him in Adventure Mode
083. Master Hand - Beat Classic Mode on Hard without using a continue
084. Crazy Hand - Beat Adventure Mode on Hard without using a continue
135. Mew - Beat All-Star Mode on Hard with continues if needed
176. F-Zero Racers - Get all 25 Smash 1 trophies
191. Battlefield - Beat All-Star Mode
204. Wario - Beat All-Star Mode without using a continue
230. Samus's Starship - Complete "Escape From Brinstar" in Adventure Mode
255. Meowth - Get all 25 Smash 2 trophies
276. Donkey Kong Junior - Complete Classic Mode with all 25 characters
280. Mach Rider - Get the Speed Demon bonus

     You get these by beating the indicated Event Matches:
104. Motion-Sensor Bomb - Clear Event Match #3
147. Entei - Clear Event Match #26
188. Game & Watch - Clear Event Match #45
192. Final Destination - Clear Event Match #51
193. Goomba - Clear Event Match #14
221. Majora's Mask - Clear Event Match #47

     You get these in the Target Test:
156. Lon Lon Milk - Beat it with everyone in under a total time of 25:00
160. Kirby Hat 4 - Get Mr. Game & Watch
189. Target - Beat it with all of the characters
288. Sheriff - Beat it with everyone in under a total time of 12:30

     You get these in the Home-Run Contest:
142. Unown - Use all of the characters to get a total distance of over 16,404ft. (5,000m.)
190. Sandbag - Hit the Sandbag over 984 ft. (300m.) with one characater
203. Paper Mario - Hit the Sandbag over 1476 ft. (450m.) with one character

     You get these in the Multi-Man Melee:
079. Male Wire Frame - Complete the 100 Man Melee
080. Female Wire Frame - KO 100 enemies in the Endless Melee
081. Fighting Wire Frames - Survive the 15 Minute Melee
269. Mr. Resetti - Beat 5 enemies in the Cruel Melee

     You get these by doing certain things in VS. Mode:
085. Food - Play 1,000 VS. Matches
086. Maximum Tomato - Play 10 VS. Matches
087. Heart Container - Play 100 VS. Matches
119. Smash Coins - Play 100 Coin Matches
141. Sudowoodo - Play 200 VS. Matches
175. Falcon Flyer - Play 150 VS. Matches
182. Kraid - Play 50 VS. Matches
186. UFO - Play 100 VS. Matches

     You get these by doing certain things in the game:
092. Lip's Stick - Get a combo of 21 or higher with one character in Training Mode
110. Metal Box - Get a combo of 11 or higher with one character in Training Mode
111. Bunny Hood - Use all of the characters to get a total of 125 combos or more in Training Mode 
151. Celebi - Release Celebi from a Pokeball
161. Kirby Hat 5 - Unlock Roy, Pichu, Dr. Mario, Young Link and Falco
220. Marin - Unlock all of the hidden characters and arenas
226. Landmaster Tank - Get over 1,000 total KO's
267. Tom Nook - Get over 1,000 total coins
274. Captain Olimar - Have a Pikmin File on your memory card
289. Diskun - Get all 249 Bonus Point Categories

     You get these randomly by finding them in 1-P Mode or winning them in the Lottery:
088. Warp Star
089. Ray Gun
090. Super Scope
091. Fire Flower
093. Star Rod
094. Beam Sword
095. Home-Run Bat
096. Fan
097. Hammer
098. Green Shell
099. Red Shell
100. Flipper
101. Freezie
102. Mr. Saturn
103. Bob-omb
105. Super Mushroom
106. Poison Mushroom
107. Starman
108. Parasol
109. Screw Attack
112. Cloaking Device
113. Barrel Cannon
114. Party Ball
115. Crate
116. Barrel
117. Capsule
118. Egg
120. Pokeball
121. Venusaur
122. Charizard
123. Squirtle
124. Blastoise
125. Clefairy
126. Electrode
127. Weezing
128. Chansey
129. Goldeen
130. Staryu
131. Snorlax
132. Articuno
133. Zapdos
134. Moltres
136. Chikorita
137. Cyndaquil
138. Togepi
139. Bellossom
140. Marill
143. Wobbuffet
144. Scizor
145. Porygon2
146. Raikou
148. Suicune
149. Lugia
150. Ho-oh
152. Toad
153. Coin
154. Vegetable
155. Megavitamins
157. Kirby Hat 1
158. Kirby Hat 2
159. Kirby Hat 3
162. Princess Peach's Castle
163. Bullet Bill
164. Lakitu
165. Pidgit
166. Birdo
167. Klap Trap
168. Shy Guys
169. Pak E. Derm
170. Tingle
171. Moon
172. Turtle
173. Four Giants
174. Master Sword
177. Mute City
178. Arwing
179. Great Fox
180. Peppy Hare
181. Slippy Toad
183. Chozo Statue
184. Whispy Woods
185. Fountain of Dreams
187. Pokemon Stadium
194. Koopa Troopa
195. Koopa Paratroopa
196. ReDead
197. Octorok
198. Like Like
199. Topi
200. Polar Bear
201. Raccoon Mario
202. Metal Mario
205. Plum
206. Daisy
207. Waluigi
208. Thwomp
209. Boo
210. Koopa Clown Car
211. Viruses
212. Bucket
213. Racing Kart
214. Baby Mario
215. Baby Bowser
216. Raphael Raven
217. Dixie Kong
218. King K. Rool
219. Goron
222. Ocarina of Time
223. Samurai Goroh
224. Dr. Stewart
225. Jody Summer
227. Wolfen
228. Andross
229. Andross
231. Metroid
232. Ridley
233. Fire Kirby
234. Fighter Kirby
235. Ball Kirby
236. Waddle Dee
237. King Dedede
238. Rick
239. Gooey
240. Meta-Knight
241. Paula
242. Jeff
243. Poo
244. Starman
245. Bulbasaur
246. Poliwhirl
247. Ditto
248. Eevee
249. Totodile
250. Crobat
251. Cleffa
252. Igglybuff
253. Steelix
254. Heracross
256. Professor Oak
257. Misty
258. ZERO-ONE
259. Maruo Maruhige
260. Ryota Hayami
261. Kensuke Kimachi
262. Love Giant
263. Hate Giant
264. Ray MK II
265. Bayonette
266. Annie
268. Totakeke
270. Heririn
271. Alpha
272. Vacuum Luigi
273. Pikmin
275. Excitebike
277. Ducks
278. Bubbles
279. Eggplant Man
281. Balloon Fighter
282. Stanley
283. Pit
284. Dr. Wright
285. Donbe & Hikari
286. Ayumi Tachibana
287. Monster
290. Nintendo GameCube

- MASTER CHECKLIST -
[ ] 001. Mario
[ ] 002. Mario (Smash 1)
[ ] 003. Mario (Smash 2)
[ ] 004. Donkey Kong
[ ] 005. Donkey Kong (Smash 1)
[ ] 006. Donkey Kong (Smash 2)
[ ] 007. Link
[ ] 008. Link (Smash 1)
[ ] 009. Link (Smash 2)
[ ] 010. Samus Aran
[ ] 011. Samus Aran (Smash 1)
[ ] 012. Samus Aran (Smash 2)
[ ] 013. Yoshi
[ ] 014. Yoshi (Smash 1)
[ ] 015. Yoshi (Smash 2)
[ ] 016. Kirby
[ ] 017. Kirby (Smash 1)
[ ] 018. Kirby (Smash 2)
[ ] 019. Fox McCloud
[ ] 020. Fox McCloud (Smash 1)
[ ] 021. Fox McCloud (Smash 2)
[ ] 022. Pikachu
[ ] 023. Pikachu (Smash 1)
[ ] 024. Pikachu (Smash 2)
[ ] 025. Ness
[ ] 026. Ness (Smash 1)
[ ] 027. Ness (Smash 2)
[ ] 028. Captain Falcon
[ ] 029. Captain Falcon (Smash 1)
[ ] 030. Captain Falcon (Smash 2)
[ ] 031. Bowser
[ ] 032. Bowser (Smash 1)
[ ] 033. Bowser (Smash 2)
[ ] 034. Peach
[ ] 035. Peach (Smash 1)
[ ] 036. Peach (Smash 2)
[ ] 037. Ice Climbers
[ ] 038. Ice Climbers (Smash 1)
[ ] 039. Ice Climbers (Smash 2)
[ ] 040. Zelda
[ ] 041. Zelda (Smash 1)
[ ] 042. Zelda (Smash 2)
[ ] 043. Sheik
[ ] 044. Sheik (Smash 1)
[ ] 045. Sheik (Smash 2)
[ ] 046. Luigi
[ ] 047. Luigi (Smash 1)
[ ] 048. Luigi (Smash 2)
[ ] 049. Jigglypuff
[ ] 050. Jigglypuff (Smash 1)
[ ] 051. Jigglypuff (Smash 2)
[ ] 052. Mewtwo
[ ] 053. Mewtwo (Smash 1)
[ ] 054. Mewtwo (Smash 2)
[ ] 055. Marth
[ ] 056. Marth (Smash 1)
[ ] 057. Marth (Smash 2)
[ ] 058. Mr. Game & Watch
[ ] 059. Mr. Game & Watch (Smash 1)
[ ] 060. Mr. Game & Watch (Smash 2)
[ ] 061. Dr. Mario
[ ] 062. Dr. Mario (Smash 1)
[ ] 063. Dr. Mario (Smash 2)
[ ] 064. Ganondorf
[ ] 065. Ganondorf (Smash 1)
[ ] 066. Ganondorf (Smash 2)
[ ] 067. Falco Lombardi
[ ] 068. Falco Lombardi (Smash 1)
[ ] 069. Falco Lombardi (Smash 2)
[ ] 070. Young Link
[ ] 071. Young Link (Smash 1)
[ ] 072. Young Link (Smash 2)
[ ] 073. Pichu
[ ] 074. Pichu (Smash 1)
[ ] 075. Pichu (Smash 2)
[ ] 076. Roy
[ ] 077. Roy (Smash 1)
[ ] 078. Roy (Smash 2)
[ ] 079. Male Wire Frame
[ ] 080. Female Wire Frame
[ ] 081. Fighting Wire Frames
[ ] 082. Giga Bowser
[ ] 083. Master Hand
[ ] 084. Crazy Hand
[ ] 085. Food
[ ] 086. Maximum Tomato
[ ] 087. Heart Container
[ ] 088. Warp Star
[ ] 089. Ray Gun
[ ] 090. Super Scope
[ ] 091. Fire Flower
[ ] 092. Lip's Stick
[ ] 093. Star Rod
[ ] 094. Beam Sword
[ ] 095. Home-Run Bat
[ ] 096. Fan
[ ] 097. Hammer
[ ] 098. Green Shell
[ ] 099. Red Shell
[ ] 100. Flipper
[ ] 101. Freezie
[ ] 102. Mr. Saturn
[ ] 103. Bob-omb
[ ] 104. Motion-Sensor Bomb
[ ] 105. Super Mushroom
[ ] 106. Poison Mushroom
[ ] 107. Starman
[ ] 108. Parasol
[ ] 109. Screw Attack
[ ] 110. Metal Box
[ ] 111. Bunny Hood
[ ] 112. Cloaking Device
[ ] 113. Barrel Cannon
[ ] 114. Party Ball
[ ] 115. Crate
[ ] 116. Barrel
[ ] 117. Capsule
[ ] 118. Egg
[ ] 119. Smash Coins
[ ] 120. Pokeball
[ ] 121. Venusaur
[ ] 122. Charizard
[ ] 123. Squirtle
[ ] 124. Blastoise
[ ] 125. Clefairy
[ ] 126. Electrode
[ ] 127. Weezing
[ ] 128. Chansey
[ ] 129. Goldeen
[ ] 130. Staryu
[ ] 131. Snorlax
[ ] 132. Articuno
[ ] 133. Zapdos
[ ] 134. Moltres
[ ] 135. Mew
[ ] 136. Chikorita
[ ] 137. Cyndaquil
[ ] 138. Togepi
[ ] 139. Bellossom
[ ] 140. Marill
[ ] 141. Sudowoodo
[ ] 142. Unown
[ ] 143. Wobbuffet
[ ] 144. Scizor
[ ] 145. Porygon2
[ ] 146. Raikou
[ ] 147. Entei
[ ] 148. Suicune
[ ] 149. Lugia
[ ] 150. Ho-oh
[ ] 151. Celebi
[ ] 152. Toad
[ ] 153. Coin
[ ] 154. Vegetable
[ ] 155. Megavitamins
[ ] 156. Lon Lon Milk
[ ] 157. Kirby Hat 1
[ ] 158. Kirby Hat 2
[ ] 159. Kirby Hat 3
[ ] 160. Kirby Hat 4
[ ] 161. Kirby Hat 5
[ ] 162. Princess Peach's Castle
[ ] 163. Bullet Bill
[ ] 164. Lakitu
[ ] 165. Pidgit
[ ] 166. Birdo
[ ] 167. Klap Trap
[ ] 168. Shy Guys
[ ] 169. Pak E. Derm
[ ] 170. Tingle
[ ] 171. Moon
[ ] 172. Turtle
[ ] 173. Four Giants
[ ] 174. Master Sword
[ ] 175. Falcon Flyer
[ ] 176. F-Zero Racers
[ ] 177. Mute City
[ ] 178. Arwing
[ ] 179. Great Fox
[ ] 180. Peppy Hare
[ ] 181. Slippy Toad
[ ] 182. Kraid
[ ] 183. Chozo Statue
[ ] 184. Whispy Woods
[ ] 185. Fountain of Dreams
[ ] 186. UFO
[ ] 187. Pokemon Stadium
[ ] 188. Game & Watch
[ ] 189. Target
[ ] 190. Sandbag
[ ] 191. Battlefield
[ ] 192. Final Destination
[ ] 193. Goomba
[ ] 194. Koopa Troopa
[ ] 195. Koopa Paratroopa
[ ] 196. ReDead
[ ] 197. Octorok
[ ] 198. Like Like
[ ] 199. Topi
[ ] 200. Polar Bear
[ ] 201. Raccoon Mario
[ ] 202. Metal Mario
[ ] 203. Paper Mario
[ ] 204. Wario
[ ] 205. Plum
[ ] 206. Daisy
[ ] 207. Waluigi
[ ] 208. Thwomp
[ ] 209. Boo
[ ] 210. Koopa Clown Car
[ ] 211. Viruses
[ ] 212. Bucket
[ ] 213. Racing Kart
[ ] 214. Baby Mario
[ ] 215. Baby Bowser
[ ] 216. Raphael Raven
[ ] 217. Dixie Kong
[ ] 218. King K. Rool
[ ] 219. Goron
[ ] 220. Marin
[ ] 221. Majora's Mask
[ ] 222. Ocarina of Time
[ ] 223. Samurai Goroh
[ ] 224. Dr. Stewart
[ ] 225. Jody Summer
[ ] 226. Landmaster Tank
[ ] 227. Wolfen
[ ] 228. Andross
[ ] 229. Andross
[ ] 230. Samus's Starship
[ ] 231. Metroid
[ ] 232. Ridley
[ ] 233. Fire Kirby
[ ] 234. Fighter Kirby
[ ] 235. Ball Kirby
[ ] 236. Waddle Dee
[ ] 237. King Dedede
[ ] 238. Rick
[ ] 239. Gooey
[ ] 240. Meta-Knight
[ ] 241. Paula
[ ] 242. Jeff
[ ] 243. Poo
[ ] 244. Starman
[ ] 245. Bulbasaur
[ ] 246. Poliwhirl
[ ] 247. Ditto
[ ] 248. Eevee
[ ] 249. Totodile
[ ] 250. Crobat
[ ] 251. Cleffa
[ ] 252. Igglybuff
[ ] 253. Steelix
[ ] 254. Heracross
[ ] 255. Meowth
[ ] 256. Professor Oak
[ ] 257. Misty
[ ] 258. ZERO-ONE
[ ] 259. Maruo Maruhige
[ ] 260. Ryota Hayami
[ ] 261. Kensuke Kimachi
[ ] 262. Love Giant
[ ] 263. Hate Giant
[ ] 264. Ray MK II
[ ] 265. Bayonette
[ ] 266. Annie
[ ] 267. Tom Nook
[ ] 268. Totakeke
[ ] 269. Mr. Resetti
[ ] 270. Heririn
[ ] 271. Alpha
[ ] 272. Vacuum Luigi
[ ] 273. Pikmin
[ ] 274. Captain Olimar
[ ] 275. Excitebike
[ ] 276. Donkey Kong Junior
[ ] 277. Ducks
[ ] 278. Bubbles
[ ] 279. Eggplant Man
[ ] 280. Mach Rider
[ ] 281. Balloon Fighter
[ ] 282. Stanley
[ ] 283. Pit
[ ] 284. Dr. Wright
[ ] 285. Donbe & Hikari
[ ] 286. Ayumi Tachibana
[ ] 287. Monster
[ ] 288. Sheriff
[ ] 289. Diskun
[ ] 290. Nintendo GameCube
[ ] 291. Tamagon - Japan Only
[ ] 292. Mario Riding Yoshi - Japanese promotion
[ ] 293. Helmet-less Samus - Japanese promotion