Would it be j'ai arrivé à faire or je suis arrivé à faire?
I know the normal form of arriver conjugates with être as auxiliary but I am not so sure about the other usage.
Arriver is one of the small group of verbs that uses être as its auxiliary for the passé composé, as you've mentioned.
"Arriver à faire qqch" is no exception. Just because arriver is being followed by some additional words here, that doesn't change its grammatical nature. It's still being used in the passé composé in the context you're asking about, and so it still uses être.
So it would be "Je suis arrivé à faire qqch."