Most of the moves Donatello shows the Pulverizer during the training montage are legitimate martial arts move, including the forward roll over the shoulder and pivoting on the feet when throwing punches and kicks. The Pulverizer, of course, performs all of the moves incorrectly showing his novice skill level.
The take down Donatello teaches the Pulverizer is called the Scissor Take Down; it is commonly found in Taekwondo, Silat, and Judo. There are many versions of the move including the Flying Scissor Take Down, a rendition that is highly popular in full contact sports such as MMA.