He is only strong with his soldiers. Avoid them, and he will die in 2 seconds with no way to fight back.
EDIT: for those who don't know what I'm talking about, I'll try to elaborate. But TL;DR ^
Most of Azir's burst is from his Q-> auto attack combo. Dodging his Q will completely nullify his burst damage.
And if you happen to get hit by his Q, the damage is actually very little. Simply walk out of his soldier's auto attack range and he cannot re-position his soldiers for another 8 seconds. Plenty of time for you to counter harass, knowing he can't hurt you until his Q is back up, or make a play. However, the latter will require some skill, calculation and experience on your part, like every single other matchup in the mid lane.
It's the same thing if he attacks with two soldiers. The only difference is that his Q and auto attacks will deal 25% more damage. However, it digs a deeper hole in his mana pool, and it will deplete his soldier stacks. Most of his damage is still from his soldier's auto attack. Simply avoid them and he still has to wait 8 seconds for his cooldown. Assuming you have vision, you can force an all in and bait out his ultimate. If you're playing a long ranged mage, his short ranged ultimate won't help him.
If you can bypass his wall with an ability, then he's doomed... In any case, he'll be down an ultimate and/or trade/harassment/kill. My point is, even in his best matchup, he can still be countered. He is still a mage and will almost always lose from an all in. And although his soldiers can deal a lot of damage, it's only if you let him by standing within it's auto attack range. By avoiding them, he has no other way of damaging you.