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.
Won after 5 consecutive loses
Reach level 50
Won under 20 moves
Reach level 35
20 games played
Won under 70 seconds
Won a game with O
10 nonconsecutive wins
70% wins of at least 10 games
5 consecutive wins
Won a game with X