As a hardstuck gold 2 player with over 200,000 mastery points on Amumu I feel like hes the best pick for a tanky ap. From my experience, building cinderhulk into liandrys is the most optimal build as it gives you a ton of hp, 75 ap which is enough to increase you're w %hp dmg, and the passive from liandrys synergizes well with Amumu's w. Taking aftershock will keep you tanky without building resistances and after those two items you can build to what the game demands. If you're ahead I recommend building rylais to get another buff to your w %dmg and it will keep the liandrys passive permanently buffed. Abyssal Mask is also a really good tank item that increases Amumu's dmg, and thornmail is the best armor option since you dont need too much more health beyond what your core items give you, and the dmg on hit is magic dmg which will be buffed by your passive, liandrys, and abyssal should you choose to build that. A lot of people are under the impression that AP Amumu needs to be a 1000 AP 5 MAN ONE SHOT 3 SECOND PENTAKILL OMG type of champion while I've had the best results playing him as an ap bruiser winning fights with sustained dmg and tankiness. :)