Azelf's naturally learned Psychic moves are lacking. Extrasensory is the only truely power Psychic attack it learns by itself. If you don't have any other Psychic Pokemon, teach it some TM's like TM 29 (Psychic), TM 30 (Shadow Ball) to give it a good advantage in that department.
If you want it to be more balanced, try some grass attacks for TM's. It can learn two good ones in TM 53(Energy Ball) or TM 86 (Grass Knot). Or maybe some Electric attacks, which it can learn quite a few of. TM 24 (Thunderbolt), TM 25 (Thunder), TM 34 (Shock Wave) and TM 57 (Charge Beam) are all good Electric type attacks to consider.
Azelf does learn some decent Normal-type moves on it's own... but they are severly ineffective for the most part. Explosion only works once, since you faint after it. Last Resort is a great attack... but only when the PP points of all of your other moves have completely run out. After that, there isn't much.
Try using some of the TM's I suggested. A good mix would be one Psychic type move, one Dark type move, one Grass or Electric type move, and Last Resort being the final move as a backup plan. That should cover most of the basics, and it gives you a great moveset to go with Azelf's good stats.