I don't have an iPad, but since I run "Droidfish" on my phone, I think I can suggest it's iOS-Pendant:
https://itunes.apple.com/us/app/stockfish-chess/id305558605?mt=8
I'm not so sure about what you are looking for. Stockfish probably is not exactly adaptive but it's quite likely the strongest there is for iOS.
I basically use a mediocre chess-app to give me a lift once in a while, if I feel I need one and when I want to witness really good chess I play Stockfish or Critter and try to improve on my "how long I can survive"-value.
I've looked at a few that claim to have AI opponents that can be adaptive, and those that can play with different styles, like aggressive, positional, etc. Please post the ipad app you like with these features, and what you like about it. There are so many to choose from! Thank you.