King Sword

While defeated The Beast the third time get the magical sphere powers go back from the second stage entrance and it unlocks the achievement (Crystal)

Prince of Persia Classic (1992)

When you started in the beginning go to the first waterfall and it unlocks the achievement (Green Retro Potion)

Prince Sword

Where you entered going inside the tank go back down where you entered there is a bug and step on it and it unlocks the achievement (Squish)

Sand Dagger

While you entered The Challenge of Wisdom Map, go down the stairs and you will see a pipe go on it and it will unlock the achievement (Cannonball)

The Sands of Time Prince Costume

Find the blue potion in the The Menagerie of the Myths map and it unlocks the achievement (Blue Retro Potion)

The Two Thrones Dark Prince Costume

Find the red potion in the The Water Bearer's map and it unlocks the achievement (Red Retro Potion)

Wall Breaker

Go underneath Mah's statue and it unlocks the achievement (Monolith)