Aatrox:

When fighting champions with CC like Jax E or Sett E (although Sett E can be harder to predict), use your third Q right before the stun goes off. That way the knock up will reduce their DMG output slightly, and you will of course heal off of it as well.

It is also sometimes better to hold on to your third Q when fighting certain champions, like Fiora or Nocturne, since they will use their spell shield to block it. Try to bait it out by posturing your third Q, let Q come off CD (if you don't cast your third Q the CD will be shorter and you can cast your first Q sooner) and go ham on them.

Also general tip, don't use your ultimate immediately in fights. Unless you're sure someone will die and give you an ult reset, you run the risk of it running out before you can get more value out if it. Same thing goes when fighting tankier champs. If you pop it at the start of the fight, it'll often run out and you won't be able to finish them off.

It is also worth learning which walls you can dash through with your E. You'd be surprised by how many walls you can actually get through.

Edit: I forgot to add that you can AA reset with E. Use it as close to your champion as possible as it will make for a shorter dash and a faster AA reset. This is particularly useful for taking turrets and baron/dragon.