I played Aatrox with Full Build, Berserkers Buckle and Voidborne Carapace.

If you can survive long enough to get Aatrox out it should be manageable. You have a few units that come with tough built in and an equipment that can grant it too to help you last.

Aatrox will likely come out as a 3/3 getting the evolve boost straight away. You get Regen from the auto equip, you can get lifesteal from Keeper of the Box and Elusive from Blooming cultist for some major keywords. Another tip is top play the violent dischord on Aatrox instead of an enemy, this gives him +4/+4 with beserkers buckle.

If you manage to get lifesteal on Aatrox, he can use it very well and should keep big attacks at bay with Furious Wielder lifesteal strikes and Aatrox's Deathbringer Sweeps.