Specifiction
Your object is to collect four pieces of a magic mirror which will make one of your dreams come true! (You get a piece of the mirror by defeating an end-of-level boss.) But things get interesting as you have competitors who want their wish to come true.
You will run into an enemy (who wants the mirror) which sends bosses against you. Once the mirror is complete, if you play in two-player mode, you both may not want the same wish!
This is resolved in anime sequences between levels. And each character has their own agenda. For example, Tetsu, the old man in the helicopter, is gay (well, everyone, himself included, calls him a "faggot" -- so much for political correctness)! He'll either want to be reunited with his lover who died 40 years ago, or to become young and beautiful again.
Team him up with the second player, such as Ash (man with a jetpack), and you will see some interesting dialogue between scenes. The same is true for other characters.