Here is the full list of all 32 Legends of Persia achievements.
Finish game in Normal and hardcore mode
Finish game in hard and hardcore mode
Finish game in easy and hardcore mode
Killing 1000 enemies
Used 50 potions
Using your skills for 500 times
Died 8 times
Died 3 times
Killed demon and released allies
Finish game in easy mode
Finish game in Normal mode
Finish game in hard mode
Killed 5th boss
Killed 4th boss
Using your skills for 200 times
Killing 400 enemies
Breaking 100 items
Using your skills for 100 times
Killed third boss
Killing 200 enemies
Earn 3000 gold
Dealing more than 12000 damage
Using your skills for 25 times
Trade first item
Killed first boss
Killed second boss
Used 10 potions
Dealing more than 5000 damage
Killing 50 enemies
Breaking 25 items
Earn 1000 gold
Earn 300 gold