To unlock
Mushroom Kingdom: in Vs. Mode, You must clear 1P Mode with all 8 Starter Characters on any difficulty with any lives without using a Continue.
Jigglypuff: Finish one player mode on any difficulty with any amount of lives and defeat him when challenged.
Captain Falcon: Finish one player mode in 20 minutes and defeat him when challenged.
Luigi: Finish the target tests for all of the first 8 characters, unlockable characters don't count and defeat him when challenged.
Ness: Finish one player mode on Normal with 3 lives and no continues, and defeat him when challenged.
And that is all you can unlock!!!