Here is the full list of all 11 Ultimate Tic-Tac-Toe achievements. It takes around 2-3 hours to unlock all of the achievements on Windows.
Reach level 50
70% wins of at least 10 games
Reach level 35
Won under 70 seconds
5 consecutive wins
20 games played
10 nonconsecutive wins
Won after 5 consecutive loses
Won under 20 moves
Won a game with O
Won a game with X