Here is the full list of all 30 Six Sides of the World achievements.
Unlock Rho Persei
Complete all the puzzles in the game
Complete, at least, one puzzle in each level
Complete all levels in Cygnus X-1
Complete Quadrangular
Complete all levels in Selene
Complete The Dark Side without moving the lights
Watch the credits
Finish the game
Complete all levels in Sirius
Complete all puzzles on the alpha, beta, gamma... levels of the game
Unlock the Unimpossible
Complete all levels in Rho Persei
Exit through the green wormhole in PAC
Unlock Sirius
Complete all levels in Altair
Complete one level in Cygnus X-1
Find all the combinations of The Safe
Complete all levels in Rao
Unlock Cygnus X-1
Unlock Altair
Complete Tau Ceti
Complete one level in Selene
Complete all the puzzles on a level with more than one
Exit through the yellow wormhole in Impossible Path
Complete a puzzle on the alpha, beta, gamma... levels of the game
Be destroyed
Unlock Rao
Unlock Selene