Here is the full list of all 12 Golden Axe achievements worth 200 gamerscore. It takes around 1-2 hours to unlock all of the achievements on Xbox 360.
You completed an online co-op game.
You beat the game without continuing.
You reached "Across the Sea" without dying once.
You beat the game in local Co-op mode.
You reached Turtle Village without dying once.
You played as every character.
You performed the Level 6 magic attack with the Amazon.
You performed the Level 3 magic attack with the Dwarf.
You beat the game.
You performed the Level 4 magic attack with the Barbarian.
You collected three potions from a thief or thieving party.
You rode the cockatrice.