Unlock Alpha Warrior:
Liberate Memory Bridge in the Yugi Story on Dream World.

Unlock Silfer's Orb:
Beat Kaiba's game to unlock Silfer's Orb.

Unlock Soul of Oblisk:
Beat Yugi's story to unlock the Soul of Oblisk.

Get the Magician of Black Chaos:
Use the Black Luster Ritual on the Dark Magician to get the Magician of
Black Chaos.

Fusions:

B. Skull Dragon = Red Eyes Black Dragon + Summoned

Skull
Blue Eyes Ultimate Dragon = Blue Eyes White Dragon X3
Crimson Sunbird = Mavelus + Faith Bird
Gaia The Dragon Champion = Gaia The Fierce Knight +

Curse of Dragon
Illusionary Beast = Gazelle + Berrformet
Magnet Valkyrion = 3 Magnet Warriors
Meteor B. Dragon = Red Eyes Black Dragon + Meteor

Dragon
Rabid Horsemen = Mystic Horsemen + Battle Ox
Thousand Dragon = Time Wizard = Baby Dragon
Twin Headed Thunder Dragon = Thunder Dragon + Two headed King Rex

Available Monsters
A list of most of the monsters in the game:

Alpha The Magnet Warrior
Anasatsu
Aqua Dragon
Aqua Madoor
Armored Lizard
Axe Raider
Baby Dragon
Barrel Dragon
Basic Insect
Battle Ox
Beast Tamer
Beaver Warrior
Beta The Magnet Warrior
Bickuri Box
Black Land Fire Dragon
Black Luster Soldier
Blue Eyes White Dragon
Buster Blader
Castle of Dark Illusions
Celtic Guardian
Crawling Dragon
Curse of Dragon
Cyber Commander
Cyber Saurus
Dancing Elf
Dark Chimera
Dark Elf
Dark Magician
Dark Magician Girl
Dark Plant
Dark Rabbit
Dark Witch
Dragon Piper
Dragon Seeker
Dunames Dark Witch
Dungeon Worm
Enchanting Mermaid
Evil Dark Magician
Fairies Gift
Faith Bird
Feral Imp
Fiend Kraken
Flame Cerebrus
Flame Swordsman
Fortress Whale
Gaia The Fierce Knight
Gama The Magnet Warrior
Garoozis
GateGuardian
Gazelle King of Mythical Beasts
Gemini Elf (Blonde)
Gemini Elf (Brunette)
Giant Insect
Giant Red Sea Snake
Giant Soldier of Stone
Giltia The D. Knight
Great Moth
Gyuketenno Megami
HaneHane
Harpie Lady (Blonde)
Harpie Lady (Blue)
Harpie Lady (Red)
Harpie's Pet Dragon
Hercules Beetle
Hitotsume Giant
Horn Imp
Hunter Spider
Illusionary Gentlemen
Ilusionist Faceless Mage
Insect Queen
Invitation to a Dark Sleep
Jelly Fish
Jinzo
Judge Man
KairyuShin
Kaiser Dragon
Kanan The Swordmistress
Kazejin
King of Yamimakai
Kuriboh
Labyrinth Tank
Larvae Moth
Launcher Spider
Lava Battleguard
Lord of D.
Magician of Black Chaos
Magician of Faith
Man Eater Bug
Mavelus
Meteor Dragon
Millenium Golemn
Mountain Warrior
Mystic Horseman
Mystical Elf
Neck Hunter
Obelisk the Tormentor
Panther Warrior
Parrot Dragon
Penguin Knight
Pumpking the King of Ghosts
Queen of Autumn Leaves
Reaper of the Cards
Red Eyes Black Dragon
Red Eyes Black Dragon
Rocket Warrior
Rogue Doll
RyuKishen Powered
Saggi The Dark Clown
Sanga of Thunder
Seiyaryu
Serpent Night Dragon
Shadow Ghoul
Silver Fang
Slifer the Sky Dragon
Slot Machine
Spike Seadra
Stuffed Animal
Suijin
Summoned Skull
Swamp Battleguard
Sword Stalker
Tao the Chanter
The Ghoul with a big appetite
The Snake Hair
The Winged Dragon of Ra
Three Headed Geedo
Thunder Dragon
Tiger Axe
Time Wizard
Twin Headed King Rex
Uraby
Water Girl
Winged Dragon Guardian #1
Zoa
Zombie Warrior