Go to the options and then go to the password screen. Next you will see 5 symbols:
Use the following keys when entering the passwords: 

L: Leonardo
M: Michaelangelo
D: Donatello
R: Raphael
S: Splinter 

Alternate Costumes:
Enter the code then hold L or R when selecting your character 

Donatello: SRSMM
Leonardo: RMMLL
Michaelangelo: DLDSM
Raphael: LMSDD 

Longer Bandanna and Double Attack Power:
Donatello: SMLLR
Leonardo: SLDDS
Michaelangelo: SMRDL
Raphael: SRRLR 

Shorter Bandanna and Double Defense Power:
Donatello: LLSMR
Leonardo: MLLSR
Michaelangelo: MRLLD
Raphael: LSMDR 

Weapon Power-Up:
Donatello: DRLDS
Leonardo: LMLSD
Michaelangelo: MSRMM
Raphael: RDSRL 

Infinite Shurikens:
Leonardo: MSSRD
Michaelangelo: MRRSL 

Master Spinter in Story mode: LLMSR
Casey Jones in Story mode: SRLMD
Alternate hit sound effects: LSLSS
Playmates toy database: LSDRM 

Challenge Mode:
Successfully complete story mode with all of the turtles. 

Casey Jones:
Complete level 1 as Raphael to unlock Casey Jones in Versus mode. 

Evil Turtlebot:
Complete level 3 with any turtle to unlock Evil Turtlebot in Versus mode. 

Hun:
Complete level 6 as Michaelangelo to unlock Hun in Versus mode. 

Oroku Saki:
Defeat Saki with any turtle to unlock Oroku Saki in Versus mode. 

Shredder:
Defeat Shredder with any turtle to unlock Shredder in Versus mode. 

Master Splinter:
Complete Dojo level 3 as Leonardo to unlock Splinter in Versus mode. 

Yoshi Hamato:
Complete Challenge Mode with any turtle to unlock Yoshi Hamato in versus mode. 

Holiday Costumes:
Set your console's system date to December 25 to see the turtles with a Christmas theme. Set the system date to October 31 to see the turtles with a Halloween theme.