From StrategyWiki, the free strategy guide and walkthrough wiki

There are 12 achievements in Teenage Mutant Ninja Turtles (arcade) worth a total of 200 .

Picture	Achievement	Description
	Lofty Goal	Clear out April's Loft, losing 10 health or less, in a Local game.	10
	Lickity Split	Clear out the Apartment and April’s Loft in 2:00 minutes or less.	10
	Fire Hazard	Rescue Master Splinter without being burned by the flamethrower.	20
	Evade	Defeat General Traag in the Technodrome, losing 20 or less health.	15
	Deep Freeze	Get past the freezing trap in the Technodrome, without being frozen.	15
	Strategy	Defeat Krang's robot, losing 10 health or less.	25
	Turtle Soup	Defeat Shredder without being turned into a regular turtle.	25
	Superhero	Destroy all Parking Meters, Pylons, Barrels, and Speed Signs in the game.	15
	Ninjitsu	Defeat three opponents with a direct attack.	10
	Slice and Dice	Earn 250 points, individually, in an Xbox Live CO-OP game.	25
	Real Ultimate Power	Defeat Shredder in an Xbox Live CO-OP game, and live to tell the tale.	30

[edit] Secret

Picture	Achievement	Description
	In the Dark	Fall into a manhole 5 times.	0