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