Here is the full list of all 37 Bright Paw achievements.
Be burned to death
Disintegrated by lasers 10 times
Find all collectables in "Manufacture"
Complete All Collectable Groups
Complete Act 9
Find all collectables in "Robotics"
Find all collectables in "Bright Paw"
Find all collectables in "The Killer"
Complete Act 8
Find all collectables in "Underground"
Find all collectables in "The Family"
Be electrocuted 5 times
Find all Security Camera Collectables
Find all collectables in "Failsafes"
Find all collectables in "Research"
Get run over 10 times
Find all collectables in "Curios"
Complete Act 7
Find all collectables in "Nathaniel"
Use all of Theo's Powers
Complete Act 6
Complete Act 5
Complete Act 4
Complete Act 3
Complete Act 2
Complete Act 1
Complete Level 10 of "The Code"
Complete Level 10 of "Escher"
Complete Level 10 of "Blockout"
Complete Level 10 of "The Subconscious Part 1"
Complete Level 10 of "The Retelling Part 1"
Complete Level 10 of "The Retelling Part 2"
Complete Level 10 of "The Subconscious Part 2"
Complete Level 10 of "Retro"
Complete Level 10 of "The Subconscious Part 3"
Complete Level 10 of "The Temples of Daz"
Complete Bright Paw's Ultimate Challenge!