Captain Falcon - Beat the game in under 15 minutes on any diffuculty.
Luigi - Beat target test with all the non secret characters.
Ness - Beat the game on Normal difficulty with 3 lives, and no continues.
Jigglypuff - Beat the game (it's okay if you continue).

Please review my answer.

To get captain falcon beat1p. mode under 5 minutes.

To get ness beat 1p. mode with 3 lives on normal.

To get luigi beat target test with all characters.

To get jiggilypuff beat the game.

Captin Falcon:
Beat the game as one of the rugular characters in under 15 min. When Captin challengs you, defeat him and he will be a playable character.

Ness:
Beat the game on Normal with the number of lives set to three and without continuing. After the creadits Ness will challenge you. Beat him and he will become playable.

Jigglypuff:
Beat 1-player mode with any character.

Luigi:
Break all the targets in 1-player practice with the 8 original characters.
(Note:You may also have to board all the platform too because i'm not sure).

P.S.Could you answer my some of my Questions and rate my answer?(I'll rate your answers!)

Jigglypuff: Beat the game (you can continue)

Captain Falcon: beat the game in 15 minutes on any diffuculty (you can continue but it wastes time)

Ness: Beat the game on normal diffuculty with three lives (you can't continue)

Luigi: Complete Break the Targets with all 8 original characters.