Quoted:

Fight or be forgotten

I am a high diamond - low master Aatrox one trick. I play in NA server and have peaked at about 450LP Master this season. I mostly only play Aatrox and have been playing the champion since Season 4.

I hit Platinum in Season 4, and hit Diamond in Season 5. Most of the matchups I have learned them through my own experience and not online. So maybe you can learn something different from the way I approach them.

Before minions spawn

If you are tryhard enough, you should guard one of the entrances to your junglers jungle. Simply to help him not get invaded and then him perma ping you and annoy you.

If you have a hook support on your team, you can invade with your team. Your level 1 isn't that great but it can work.

If they have a hook support, you can camp a bush with your team. Or just ego it and walk straight to your tower and go grab a drink or something.

Be patient

Be a stoic. Realize you lack power right now. Embrace zen. Keep the enemy top away from you. Trade/ poke well and get the CS you can get. If you can, have your jungle path away from you, or hope for a counter gank.

Still there are some lanes you can play aggro in (like Nasus). In those lanes you should get prio. If you do ward the bush before 3, so you can prevent being ganked.

Go DShield if you want a more guranteed easier level 1 - 3.

You are becoming Aatrox

You spike with every level. Every point in Q is hell you inflict on the enemy laner. Make him regret queing up. Play aggressive. But also play matchup dependant. Look for plays, outplays, 1v2s. Know your limits and play aggressive.

At Level 9 and Level 11 you are THE WORLD ENDER. Make them regret breathing the same air as you.

Look for opportunities

At this time, you should have your tower. If not, they probably have your tower. Look around the map, see objectives. Try to read what the enemy team is doing. Show up. Be there.

Also keep up in farm. That means collecting side lanes when its safe to do. With TP, keep pressure up in the sidelane away from the next contestable objective.

You are at the Mercy of Riot Games

Once everyone has 3 items. You have to play like Faker. There will be too much CC, too much damage, and alot of unpredictability. It'll be easier for you if you have a primary engage, because you wasting your E to get in range and maybe missing a crucial ability or someone flashing out or dashing out will be death for you.

If you go pure bruiser, you will have more survivability. But your purpose usually is front to back, and sometimes you can flank and get the backline. But it's not as easy as an assassin because you have limited range, and no way to get out.

Rely on you ult resets. Know your limits.

Ward
Put down wards,
Put down red wards.

They are not for you, they are for the muppets that play with you. So they won't walk in a bush and die for no reason.