Ghost, Dark and Bug.
A recommended moveset for Azelf is:
Thunderbolt
Flamethrower
Psychic
Shadow Ball
That deals with all of it's weakneses.
Chat with our AI personalities
Ghost & Flying. I believe that's it! Not dark or bug because although they're super-effective against Psychic, they are not-effective against Fighting. And not Psychic, because though it's super-effective against Fighting, it's not-effective against Psychic.
electric and ice are effective against flying
Azelf is a legendary Pokemon.
Water and Grass attacks are super effective against Onix.
Dragon types are gods, nothing is effective against dragon