Here is the full list of all 23 Jigsaw Puzzles Infinite achievements.
Finish 10 puzzles
Complete a puzzle with at least 100 pieces under 3 minutes
Connect a total of 1000 pieces
Finish 5 puzzles
Finish 5 unique puzzles
Add 1 custom puzzle
Finish 1 puzzle
Finish a classic puzzle (over 200 pieces) without sorting (spreading pieces is fine)
Connect a total of 100 pieces
Finish 25 puzzles
Finish 50 puzzles
Finish 100 puzzles
Finish 10 puzzles in Zen mode
Finish 10 puzzles in Classic mode
Finish 20 Unique puzzles
Finish 50 Unique puzzles
Finish 2 puzzles with unique shapes
Finish 5 puzzles with unique shapes
Finish a puzzle with at least 1000 pieces
Connect a total of 10000 pieces
Add 5 custom puzzles
Add 10 custom puzzles
Finish a zen puzzle with at least 100 pieces without mistakes (puzzle never lands on board)