Here is the full list of all 13 Silicon Zeroes achievements.
Beat the first board.
Beat the game.
Beat the final ending.
Beat all puzzles.
Perfect all puzles.
Find the secret board.
Beat 'Threes'.
Beat 'Multiply'.
Beat the secret board.
Beat an 'ideal' score.
Beat the second board.
Beat 'Faux-Reg' variants 1, 2 and 3.
Beat 'Cows'.