Here is the full list of all 95 Jigsaw Savant achievements.
Complete 1 story stage
Complete 5 story stages
Complete 10 story stages
Complete 20 story stages
Complete all story stages
Complete 1 challenge stage
Complete 5 challenge stages
Complete 10 challenge stages
Complete 20 challenge stages
Complete all challenge stages
Complete 1 bonus stage
Complete 5 bonus stages
Complete 30 bonus stages
Complete 40 bonus stages
Complete 50 bonus stages
Complete 70 bonus stages
Complete all bonus stages
Complete 10 bonus stages
Complete 20 bonus stages
Unlock Bonus Stage 1
Unlock Bonus Stage 2
Unlock Bonus Stage 3
Complete 1 Stage At Easy Difficulty
Complete 5 Stages At Easy Difficulty
Complete 10 Stages At Easy Difficulty
Complete 20 Stages At Easy Difficulty
Complete 30 Stages At Easy Difficulty
Complete 50 Stages At Easy Difficulty
Complete 100 Stages At Easy Difficulty
Complete All Stages At Easy Difficulty
Complete 1 Stage At Normal Difficulty
Complete 5 Stages At Normal Difficulty
Complete 10 Stages At Normal Difficulty
Complete 30 Stages At Normal Difficulty
Complete 50 Stages At Normal Difficulty
Complete 100 Stages At Normal Difficulty
Complete All Stages At Normal Difficulty
Complete 20 Stages At Normal Difficulty
Complete 1 Stage At Real Difficulty
Completed 5 Stages At Real Difficulty
Completed 10 Stages At Real Difficulty
Completed 20 Stages At Real Difficulty
Completed 30 Stages At Real Difficulty
Completed 50 Stages At Real Difficulty
Completed 100 Stages At Real Difficulty
Complete All Stages At Real Difficulty
Complete 1 stage with 36 pieces
Complete 10 stages with 36 pieces
Complete 20 stages with 36 pieces
Complete 30 stages with 36 pieces
Complete 50 stages with 36 pieces
Complete 100 stages with 36 pieces
Complete all stages with 36 pieces
Complete 1 stage with 65 pieces
Complete 5 stages with 65 pieces
Complete 10 stages with 65 pieces
Complete 20 stages with 65 pieces
Complete 65 stages with 65 pieces
Complete 100 stages with 65 pieces
Complete all stages with 65 pieces
Complete 1 stage with 126 pieces
Complete 5 stages with 126 pieces
Complete 10 stages with 126 pieces
Complete 20 stages with 126 pieces
Complete 30 stages with 126 pieces
Complete 50 stages with 126 pieces
Complete 100 stages with 126 pieces
Complete all stages with 126 pieces
Complete 1 stage with 260 pieces
Complete 5 stages with 260 pieces
Complete 10 stages with 260 pieces
Complete 20 stages with 260 pieces
Complete 30 stages with 260 pieces
Complete 50 stages with 260 pieces
Complete 100 stages with 260 pieces
Complete all stages with 260 pieces
Complete 1 stage with 429 pieces
Complete 5 stages with 429 pieces
Completed 10 stages with 429 pieces
Completed 20 stages with 429 pieces
Completed 30 stages with 429 pieces
Completed 50 stages with 429 pieces
Completed 100 stages with 429 pieces
Completed all stages with 429 pieces
Complete all story, challenge and bonus stages!