Here are some (if not all) passwords for the game.

Enter the following at the password screen:

Infinite Shuriken : RSRLRSM
Cheat Code Health : DSRDMRM
Nexus outfit for Leonardo : LMRMDRD
Endurance - Life doesn't heal : MRMDRMD
Nexus outfit for Raphael : RMSRMDR
Nexus outfit for Michelangelo : MLMRDRM
Nexus outfit for Donatello : DSLRDRM
Playmates added to Bonus Materials : SRMLDDR
Super-Tough : RDSRMRL
Toddling : SSSMRDD
Super Defense Power (Defense x2) : LDRMRLM
Self Recovery : DRMSRLR
Super Offense Power (Attack x2) : SDLSRLL
Squeaking : MLDSRDM
Poison : DRSLLSR
Pizza Paradise : MRLMRMR
Nightmare : SLSDRDL
Lose Shuriken : RLMRDSL
Fatal Blow : LRSRDRD
Abyss : SDSDRLD
Mighty Turtle : LSDRRDR