Most achievements are story line based, which makes the 1000 gamerscore easy.
Mystical Jungle
20G
Complete Level 1
Guide See Winter's Secret
Vigilantism
24G
Complete Level 2
Guide See Winter's Secret
Techno Ninjutsu
28G
Complete Level 3
Guide See Winter's Secret
Note This is also the level where you use Donatello's special move. This will unlock Used Dons special move (see the achievement for further details).
Cowabunga Carl Getaway
32G
Complete Level 4
Guide See Winter's Secret
Note This is also the level where you use Michelangelo's special move. This will unlock Used Mikes special move (see the achievement for further details).
Spirit of the Forest
36G
Complete Level 5
Guide See Winter's Secret
Note This is also the level where you use Leonardo's special move. This will unlock Used Leos special move (see the achievement for further details).
Ninja Tag Time
40G
Complete Level 6
Guide See Winter's Secret
Note This is also the level where you use the co-operative special move. This will unlock Family Unit (see the achievement for further details).
The Game is the Foot
44G
Complete Level 7
Guide See Winter's Secret
Foot trail
48G
Complete Level 8
Guide See Winter's Secret
Tower Power
52G
Complete Level 9
Guide See Winter's Secret
When the slime comes
56G
Complete Level 10
Guide See Winter's Secret
O brother where art thou
60G
Complete Level 11
Guide See Winter's Secret
Note This is also the level where you use Raphael's special move. This will unlock Used Raphs special move (see the achievement for further details).
Bite me!
64G
Complete Level 12
Guide See Winter's Secret
All is Forgiven
68G
Complete Level 13
Guide See Winter's Secret
Ninjas in the crypt
72G
Complete Level 14
Guide See Winter's Secret
The Mysterious Leader
76G
Complete Level 15
Guide See Winter's Secret
Winter's Secret
80G
Complete Level 16
Guide Every Complete Level x achievement are basically storyline achievements, and will unlock as you progress through the game and beat every level. The game is pretty easy; the enemies are weak, and there are several checkpoints throughout every level. There are several approaches to win the battles. You could use the button mashing technique, or you could use a few attacks. I found it to be easier to just hold B for a few seconds and then releasing it whenever enemies started swarming the screen, as that will launch an attack that automatically targets 5 different enemies (you actually don't have to do anything except holding B then releasing it.)
Boss battles I would recommend that you use either Michelangelo or Raphael during the (final) boss battles, because their special moves takes short time to execute than Leonardo's and Donatello's. During the boss battles the bosses will try to execute their special moves, and to cancel them, you will have to execute the turtle's special moves. In between the boss battles, the fourth boss will launch lightning attacks against you, which you will have to run in between to avoid.
First battle (General Aguila, actually Gato, but I'll use Aguila.) His attack cycle is sliding from side to side two times (stay on his opposite side), then throwing a couple of blades at you that you just have to jump over. When he starts crouching down, wait one second then jump, because he will launch a quick attack against you. If you successfully dodged his attack, all you have to do is keep hitting him until he repeats his cycle. At some point, he will jump into the middle of the arena to execute his special move, and at this point run up to him and hold down X to execute a special move and cancel out Aguila's.
Second battle (General Mono) Mono will use his hammer to create shockwaves that, upon touching them, will damage you. To avoid them, stand near the edge of the platform and then run in between them. Once he's done that a few times, he will start jumping up into the air, and try to land on your head. Just keep running around on the platform, his landing spot will be indicated by his shadow. Once he lands, you are free to hit him at will. When he falls on his back, he will get up and jump to the back of the platform to launch his special move, cancel this out, because it will kill you instantly!
Third battle (General Serpiente) She will start off by spitting some green substance at you three times, which you have to run from side to side to dodge. Once she's done that, she will slide against you to attack you, just like Aguila. Do a double-jump to avoid this attack, then attack her. And just as Aguila, she will at some point go into the middle of the platform to launch her special move. Cancel it out quickly, and keep hitting her until she dies.
Fourth battle (General Gato, actually Aguila!) To beat him you will have to use every turtle's special attack, starting with Michelangelo, then Donatello, then Raphael. If you manage to hit him with three special moves, he will fall to his knees and you will have to use Leonardo's special move to finish him off. You will need to use the special moves quickly, because if you fail, he will launch a special move. In between the cycles, fireballs will fall from the sky. The battle is pretty easy, just keep an eye out for the indication of which turtle's special move you have to use.
Video
Get your first coin
15G
Get your first coin
Guide The coins that are being referred to are actually not the silver coins you find everywhere throughout the game. The coins you need to find are gold coins shaped like a turtle shell, and will only appear in a level after you've beaten it at least once. The coins are actually not hard to find, and on your first playthrough on a level, you can spot their locations as there are a shadowy turtle shell in their place. On your next playthrough the shadowshaped shell will be swapped with an actual gold coin. This is easiest to get on the first level.
Family Unit
15G
Do a co-op move combination attack
Guide The co-operative attack can be used after level 6. To execute it, you will need to hold X for a short while until another turtle comes to your aid. Although, you will not need to use the attack for the achievement to unlock, there's also a co-operative move that will have another turtle come down to throw the turtle you're controlling a somewhat long distance. To use it, simply press A to jump once, then X to be thrown.
Used Mikes special move
30G
Used Mikes special move
Guide Michelangelo's special move is rotating his nunchuks to create a rotating helicopter blade effect. This will make him descend slowly while in air, and helps you "fly" over great distances. To use it, simply jump and hold down the Right Bumper.
Used Raphs special move
30G
Used Raphs special move
Guide Raphael's special move is using his sais to climb up red "painted" walls. Although being able to use this special move when Raph is the Nightwatcher, it will not unlock before you're doing it when Raphael is simply Raphael, and this is not be possible before level 11. To execute, run up to a wall that is glowing red, and hold down Right Bumper.
Used Leos special move
30G
Used Leos special move
Guide Leonardo's special move is "sliding" through bars. The first time you will have to do this is in level 5, and all you have to do is run up to the bars and the press Right Bumper.
Used Dons special move
30G
Used Dons special move
Guide Donatello's special move is using his bo stick to vault over a long distance. You can do this is level 3, and as with every other special move, it is executed by holding down Right Bumper.
Clean Sweep
50G
Complete a level without taking damage
Guide This is easiest to do on level 1. The few enemies on the level are towards the end (which also makes it suck if you mess up!). Also, supposedly, if you fall down from a ledge high above, you might lose health, and this will mean that you've taken damage, so avoid that!