Here is the full list of all 16 Escape Goat achievements.
Visit each room in the Prison of Agnus.
Complete The Final Path.
Beat Engine of Insanity Room 4 destroying all Reapers.
Beat Ruins of Red Clay Room 1 without touching the Skull Switch.
Beat The Darkest Pits Room 4 without harming any Reapers.
Beat The Crypt Room 5 without waking the Gargoyles.
Beat Lost City Room 5 destroying all reapers, but without disturbing the central stack of blocks.
Beat room Engine of Insanity Room 3 before the stone block falls to the floor.
Beat room Limestone Quarry Room 1 without activating any Skull Switches.
Beat room Electric Lab Room 3 without touching any of the top four switches.
Beat room The Final Path Room 1 without touching any switches or skulls.
Beat The Final Path Room 9 without destroying all TNT blocks.
Beat Frozen Cavern Room 4 with 5 Ice Blocks remaining.
Beat Frozen Cavern Room 5 without touching any of the Skull Switches.
Beat The Darkest Pits Room 5 destroying all Reapers.
Complete the Prison of Agnus in under 45 minutes.