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