I haven't had the pleasure of fighting a good PT yet.
I do believe that he is an awesome character and should be a lot higher on the tier list.
Just looking at statistics and a gut feeling though this is what I say:
He is light, good air movement, really fact moves and kills at mid high percents. His u-tilt combo's into itself for a tilt lock and since we are a FF a bet that we get hurt from that.
I guess the importance of this match up is spacing with Bair. Unless I am wrong it out range's him.
Also, FSmash him if he is in the air. BW to one side out of his attack and FSmash directly behind you. Since he is landing with an attack he can punish with a shield.
You can also try and use Vanish when he close's in. Just don't get predictable on where you are going to reappear. Also try and cancel it.
Needle's are good for messing up his shell shifting.
Chain at the ledge limits what he can do as well.
Ivy has few options for getting back onto the stage. He has a slow fair, Razor Leaf for planking, Nair and maybe Bullet Seed (IDK).
My focus would be knocking him off of the stage and not letting him back at lowish percents. When you can knock him away more you should follow up with this:
Needle Glide> Needle Cancel> Chain hog
That is an INCREDIBLY fast way of chain hogging. If you chain hog he will be lucky to knock yo off.
A fast faller that is heavy. Also, a scary dragon. O-o
Try and chain him at the ledge. Also, f-tilt> DSmash wouldn't be a bad idea.
I also believe that a non decayed Swan Combo works on him (like DK).
Needle's would help too. That and out spacing with Bair.
Just what I think would be effective. Correct me if I'm wrong since these were just stabs in the dark at how to fight them.