These are locations in Max's adventure mode.
This is the dimension that Dr. Mario lives in. Once you enter, You'll be greeted by Dr. Mario himself.
In this level(as in all levels), you must fight not only Tabuu's forces, but also the enemies native to that dimension. The first trophified character you come across is Diddy Kong, in order to get Diddy kong to join your party you must revive him. Along the way, you'll come across a dark purple door with Black Shadow's face on it. These dark purple doors always mark a match against a false character, in this case, False Black Shadow. Entering these doors is always optional, but it's the only way to get certain characters to join your party.
After the match, the next two characters you can revive are Megaman and Louie. The stage ends with a cutscene in which Bowser Jr. comes across and revives Bowser.
Baby Mario's Time Line
This time instead of traveling to an other dimension, you travel into the past to meet up with Baby Mario.
This location has only one level. Again you must fight through not only Tabuu's forces, but also the enemies native to this time line. The level is very similar to levels played in Yoshi's Island. Along the way you encounter the trophies for Lanky Kong, Captain Falcon, Crash Bandicoot and Yoshi. The level ends with a standard match against False Ganondorf. Afterward is a cutscene in which Ganondorf is revived and he and Baby Mario join your party. However, Mewtwo is hesitant to allow Baby Mario to join, fearing the damage that might done if Mario if removed from the time stream as a baby. Bowser claims that as long as Baby Mario is returned to his own time line within 24 hours after his disappearance from it(within 24 hours after he joined your party) there should be little to no damage to the time stream.
This level is one of only two levels that ends in a false character match.
Toon Link's Dimension
Your next stop is Toon Link's dimension.
In the this level, you have the chance to grab the Ice Climbers, Gooey, Samus and Ness trophies. In a cutscene at the end of the level, the team encounters the R.O.B. trophy, but before they can revive R.O.B., Porky attacks. This level ends with a boss battle against Porky. The cutscene after this shows the team reviving R.O.B..
This level ends with Bowser and Bowser Jr. explaining to Toon Link the situation and Toon Link agrees to help.
The Prince of Persia's Dimension
Your next stop is Persia, where you meet up with the Prince. This location has only one level and is pretty straight forward, but it's probably hardest level yet.
In this level, you have the chance to grab the Dixie Kong, Mario and Saki Amamiya trophies. You then come across the trophified Pokemon Trainers, but, as always, before you can revive them, you're attacked by another boss, Trion. After you defeat Trion, you revive them and make your way to the next location.
The Prince, after fighting evil gods and zombies, decides to join your party to offer his expertise.
Your next stop is the famous Planet Bomber, home of Bomberman. It has only one level regrettably, but it's a nice one.
In this level, you have the chance to grab the trophies of Peach, Roy, Fox and Luigi. It ends with a boss battle with Galleom 2.0 and after which, you revive Ike.
In the ending cutscene, Bomberman agrees to help you on your quest to defeat Tabuu once and for all as he is afraid of what might happen to his beloved home world.