Despair, Destroy and Repair

It will take some time for me to be able to solve it. But you can play with a ps4 controller if you have steam installed:

1. Launch Steam.
2. Click the Games menu, choose Add a Non-Steam Game to My Library.
3. Browse for games on your computer or put a check next to the game(s) you wish to add to the Library.
4. Click on Add Selected Programs .

This should make the ps4 controller mapping:

Square/Circle - Action

X-Jump

Hold Triangle - Restart Level

Dpad/Joystick - Move