Here is the full list of all 33 Ancient Go achievements.
Open Options Menu
Launch Basics
Capture 1 Stone
Capture 3 Stones
Win Playing 13x13
Win Playing 19x19
Capture a Group of 4
Capture a Group of 9
Capture a Group of 16
Capture a Group of 25
Lifetime Captures 50
Lifetime Captures 100
Lifetime Captures 250
Lifetime Captures 500
Lifetime Captures 1000
Play the First Move of Game in Upper Right 10 Times
Atari a Stone
Atari 2 Stones in 1 Move
Play an Atari Move 4 Turns in a Row
Connect 49 Stones
Connect Opposite Sides of the Board
Connect All 4 Sides of the Board
Win 10 Games
Win 25 Games
Win 50 Games
Win 100 Games
Lose 50 Games
Win 3 Games in a Row
Win 19x19 after Opening on Tengen
Win Losing 0 Stones
Win Despite Opponent Capturing 25 Stones
Win 5 Games in a Row
Turn Off Hints