How he found Krang, ended up in New York, and turned the Foot into a robot army isn't spelled out in the cartoon (as far as I remember at least), but he took on the name of the Shredder and covered his armor with a multitude of blades. Before we get to his powers, let's take a look at the Foot since they're with him so much.
Another benefit of his training seems to be some real super strength. In episode 7, The Incredible Shrinking Turtles, he defeats each of them one by one, but the real feet is breaking a massive wooden beam in half with one chop if his hand.
In other episodes, he's shown to chop through a branch he was standing on with one chop, bend iron bars of a cell, kick down a metal door, and twice slice a punching bag in half after throwing it into the air. I'm not sure what part of ninja school teaches you that, but it's damned impressive.
Shredder does have his drawbacks, though. His anger frequently gets the better of him, letting the calmer Splinter defeat him, like in the episode Shredder and Splintered. He loses his patience and gets real sloppy. He's also terrible with guns. The few times he's picked up a rifle or pistol, he can't hit anything. Granted, no one else in the cartoon has good aim either, but it's something to consider if Shredder loses the upper hand.
Be sure to come back next week to see his opponent, Sky Commander's General Plague. Click here to see how Bad Guy Beatdown is going so far.