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 rode the cockatrice.
Play as every character.
Choose any character and reach Turtle Village (Stage 3) without dying once.
Perform the Level 6 magic attack with the Amazon.
Perform the Level 3 magic attack with the Dwarf.
Perform the Level 4 magic attack with the Barbarian.
Collect three potions from a thief or party of thieves.
Choose any character and reach "Across the Sea" (Stage 5) without dying once.
Beat the game in local Co-op mode.
Complete an online co-op game.
Beat the game.
Beat the game without continuing.