Here is the full list of all 54 The Conquest of Go achievements.
Play the connection shape 20 times
Capture 10 stones
Capture a 4 stone or larger dragon
Capture an 8 stone or larger dragon
Play the bamboo joint shape 20 times
Play the bamboo joint shape 100 times
Play the bamboo joint shape 500 times
Play a hane shape 20 times
Play the hane shape 100 times
Play the hane shape 500 times
Play the nobi shape 20 times
Play the nobi shape 100 times
Play the nobi shape 500 times
Play the connection shape 100 times
Play the connection shape 500 times
Play the cut shape 20 times
Play the cut shape 100 times
Play the cut shape 500 times
Play the attachment shape 20 times
Play the attachment shape 100 times
Play the attachment shape 500 times
Play the one-space jump shape 20 times
Play the one-space jump shape 100 times
Play the one-space jump shape 500 times
Play the atari shape 20 times
Play the atari shape 100 times
Play the atari shape 500 times
Play the turn shape 20 times
Play the turn shape 100 times
Play the turn shape 500 times
Play the shoulder hit shape 20 times
Play the shoulder hit shape 100 times
Play the shoulder hit shape 500 times
Win your first match
Win 30 matches
Win 100 matches
Win 300 matches
Capture 100 stones
Capture 250 stones
Capture 500 stones
Play 100 stones
Play 1000 stones
Play 5000 stones
Play 10,000 stones
Conquer your first territory on the campaign map
Conquer 5 territories on the campaign map
Conquer 10 territories on the campaign map
Conquer all territories on the campaign map
Capture a 14 stone or larger dragon
Capture a 24 stone or larger dragon
Complete 20 campaign fortification puzzles
Complete 80 campaign fortification puzzles
Complete 200 campaign fortification puzzles
Complete 400 campaign fortification puzzles