Here is the full list of all 29 Wild Dogs achievements.
Defeat the third boss
Defeat the eleventh mini-boss
Defeat the tenth mini-boss
Defeat the second boss
Defeat the ninth mini-boss
Defeat the eighth mini-boss
Pilot the Mark I
Defeat the seventh mini-boss
Defeat the sixth mini-boss
Defeat the fifth mini-boss
Defeat the first boss
Defeat the fourth mini-boss
Defeat the third mini-boss
Defeat the second mini-boss
Defeat the first mini-boss
Get your first kill
Defeat the twelfth mini-boss
Defeat the thirteenth mini-boss
Defeat the fourteenth mini-boss
Defeat the fifteenth mini-boss
Defeat the sixteenth mini-boss
Defeat the fourth boss
Defeat the seventeenth mini-boss
Find a new friend
Pilot the Mark II
Defeat the fifth boss
Defeat the final boss
Finish the game