Here is the full list of all 33 Ancient Go achievements.
Turn Off Hints
Play an Atari Move 4 Turns in a Row
Atari 2 Stones in 1 Move
Atari a Stone
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
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