Hacked one of each kind of machine.

Defended yourself against Lamb's assault in the train station.

Found your way back into the ruins of Rapture.

Defeat Zeus

Battle your way to the Loom Chamber in under 10 minutes

Max out all Weapons and Magic

Awaken the Phoenix

Open the wings of the Temple of the Fates

Win the battle outside of the Palace of the Fates

Find five treasures

Kill 30 enemies with headshots

Acquire the Icarus Wings