Here is the full list of all 43 Mr. Bree+ achievements.
Get Jump
Get Crouch
Get Run
Get Wall Jump
Get Double Jump
Collect the first bad memory
Collect 5 bad memories
Collect 20 bad memories
Collect all bad memories
Beat 5 levels
Beat 20 levels
Beat 40 levels
Defeat the forest boss
Defeat the slaughterhouse boss
Beat 5 levels without dying
Beat 20 levels without dying
Beat 40 levels without dying
Beat all levels without dying
Beat your best time 10 times
Beat your best time 20 times
Die 1 time
Die 50 Times
Die 100 Times
Die 5 times in the same level
Die 10 times in the same level
Beat the tenth level
Quit a level
Enter the first slaughterhouse level
Press the red button!
Perform your first double jump
Stay still for a while
Die on the first level
Get 50% of all achievements
Get 75% of all achievements
Get all other achievements
Skip the last cutscene
Watch the credits cutscene to the end
Start a level in hardcore mode
Beat 5 levels in hardcore mode
Beat 20 levels in hardcore mode
Beat 40 levels in hardcore mode
Beat level 24 in less than 29 seconds
Complete all levels in all game modes