Here is the full list of all 15 Sudocats achievements worth 1,000 gamerscore. It takes around 1-2 hours to unlock all of the achievements on Xbox One.
Complete 1 level
Complete levels 1 - 3 in 4x4 mode
Complete 5 base levels
Complete levels 4 - 6 in 4x4 mode
Complete levels 1 - 3 in 6x6 mode
Complete 10 base levels
Complete levels 4 - 6 in 6x6 mode
Complete 15 base levels
Complete levels 7 - 9 in 6x6 mode
Complete levels 1 - 3 in 9x9 mode
Complete levels 4 - 6 in 9x9 mode
Complete levels 7 - 9 in 9x9 mode
Complete levels 10 - 12 in 9x9 mode
Complete all 27 base levels
Complete all extra puzzles