Instructions
Clear out as many bad guys as you can. Mario needs to have as much danger-free space in front of him as possible to execute a front flip.
Start out running at full speed and jump, continuing to go full speed through the air.
The moment you land, immediately jump again while continuing to go full speed. If you do it quickly enough, Mario's second jump will be slightly different than his regular jump.
Immediately jump again when you land and continue going forward at full speed. This should result in a front flip.