Here is the full list of all 43 Mr. Bree+ achievements.
Beat 5 levels without dying
Beat 40 levels
Die 100 Times
Perform your first double jump
Get Double Jump
Get Wall Jump
Beat 20 levels
Die 50 Times
Die 10 times in the same level
Beat the tenth level
Get Run
Collect 5 bad memories
Beat 5 levels
Get Crouch
Quit a level
Collect the first bad memory
Get Jump
Die 5 times in the same level
Stay still for a while
Die on the first level
Die 1 time
Collect 20 bad memories
Collect all bad memories
Defeat the forest boss
Defeat the slaughterhouse boss
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
Enter the first slaughterhouse level
Press the red button!
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