His punishes are also basic as well. You need to know how to do grab release anti-airs off of a ground grab, and if the opponent is slow enough, you can finish off with an aerial or his neutral b (can only get 1 hit though if the opponent is fast at mashing). He has 1 infinite off of his low wall attack, so you can hit an opponent OTG (off the ground) with it and combo into his anti-air (even two of them if timed correctly). From there you repeat the sequence until you get a full slam meter, but the ideal situation is to confirm it into his slam, which basically means hitting an anti-air to fill the slam meter and then use the slam.
His slam can be extended by mashing b at the correct time intervals even up to 9 seconds, so be sure to learn that when forced to land his slam in the neutral.
The rest of the character that I could mention applies to any Super Slam character, so you can just learn basic strategies, and most of them will apply to Quasimodo.
He must be the chosen one, so long as the boot fits.
He's able to pull off the Noino Boost anti air infinite just like Shrek.
To explain what's going on here, Shrek (or in the intended case Quasi) performs a low wall attack while the opponent is stunned on the floor. In a couple of frames around the point of contact you can input a shield and instantly halt your momentum whilst the opponent is popped up into the air. Here you can catch them with an anti-air which leaves them floored and in a state to repeat the combo.
(EDIT: I should say, the frame window for inputting the shield and getting the desired effect is quite tight. Too early and the attack won't connect, too late and you'll retain your momentum and be out of position to punish)