Here is the full list of all 14 Alexia Crow and the Cave of Heroes achievements.
Solve the crystal stones puzzle
Solve the minotaur maze
Solve the puzzles of the atlantis initiative
Place the two golden crosses in Typhoon cave
Complete the 4 horses puzzle
Complete the clock puzzle in the first level
Place the 3 objects on the Chronos room
Get the two keys of the game
Create the two magic stones
Solve the puzzle that envolves the sphere pilars
Play the lira a song that Hermes like
Solve the puzzle that helps Heracles to defeat the ciclops
Solve the 4 puzzles in the Gaia room
Complete the first two puzzles and open the main gate