Story Mode
This has 12 Chapters and includes basic matches and some very easy mini-games.
S.T.a.R. Labs Missions
This is basically the missions mode of the game. Every character has a set of 10 challenges which includes regular matches and mini games. The locked challenges can be unlocked by gaining stars. Aside from the Achievements that you can get, here are the costumes that can be unlocked in this mode.
Elseworld Flash = Finish all S.T.a.R. Labs missions with 3 stars.
Kryptonite Lex Luthor = Finish all S.T.a.R. Labs missions.
New 52 Shazam = Finish all of Shazam's S.T.a.R. Labs Missions.
Battles Mode
In this single player campaign, you get to choose a set of battles with pre-determined rules and randomly-picked enemies. The battles may allow you to pick your own character or not depending on the rules. Some battles types can be unlocked in the Archives Section.
Classic = Default
Fight 8 random enemies. The character you used to complete this unlocks his or her ending scene. This also unlocks Grundy's Boss Skin the first time you beat it.
Heroes Only = Default
Fight 8 random heroes on set difficulty.
Villains Only = Default
Fight 8 random villains on set difficulty.
Poisoned = Default
Fight 10 random enemies while you are poisoned.
Survivor = Default
Fight 10 random enemies while you carry over one health meter to the next match, replenishing only when you've performed skillfull gameplay.
Mirror Match = Unlocked in Archives - Extras - panel B3 - one access card
Fight yourself's same character in a series of matches.
Mystery = Unlocked in Archives - Extras - panel C2 - one access card
Fight a series of matches while gaining a buff or de-buff in between matches.
Fully Charged = Unlocked in Archives - Extras - panel A5 - one access card
Fight a series of matches while both characters has full super meters but Super Moves are banned.
Combo Heaven = Unlocked in Archives - Extras - panel B2 - one access card
Fight a series of matches while you can only deal damage by getting a specific number of required hits in a combo. Transitions and Supers are banned.
Help From Above = Unlocked in Archives - Extras - panel A4 - one access card
Fight a series of matches with the enemy's health fully regenerating every 30 seconds.
Injured = Unlocked in Archives - Extras - panel A1 - one access card
Fight a series of matches while only limited with 1/4 health at the start of every match.
Give and Take = Unlocked in Archives - Extras - panel C3 - one access card
Fight a series of matches with both characters gaining back health with every successful hit. Time limit is 90 seconds.
Sidekick = Unlocked in Archives - Extras - panel B4 - one access card
Fight a series of matches while fighting two enemies on every arena.
Speed Run = Unlocked in Archives - Extras - panel A3 - one access card
Beat all enemies within 3 minutes. Transitions and Interactibles increase the time limit.
Random Fighter = Unlocked in Archives - Extras - panel C1 - one access card
Fight a series of matches using a random character.
Countdown = Unlocked in Archives - Extras - panel A2 - one access card
Fight a series of matches with a time limit of 30 seconds per each match.
Unstoppable! = Unlocked in Archives - Extras - panel B1 - one access card
Fight a series of matches without losing a single match once.
The Max = Unlocked in Archives - Extras - panel C5 - one access card
Fight a series of matches on the hardest difficulty.
Full House = Unlocked in Archives - Extras - panel C4 - one access card
Beat all 24 characters in 24 matches.
Impossible! = Unlocked in Archives - Extras - panel B5 - one access card
Beat all 24 characters in 24 matches using a single health bar.