Predecessor Builds > Aurora > Solo Lane Assassin. Run. Them. Down.
This is my core build for Aurora. The first three items are core items and I wouldn't change these out. The last three are the strongest I've found that pair together for attack speed and ability damage. It builds around weaving her two abilities in with your basic attacks to stack your passive and get your attack speed up quickly. You will be able to chase almost everyone in the game down when landing your RMB and close the gap with your E. To run them down, you use your Q, or use it to block their escape route.
You can swap out Magnify for Lifebinder as a situational if you feel you need the omnivamp. I would choose this if they have double ranged in duo lane (Wrath/Belica for instance). Lifebinder will allow you to solo Primal Fangtooth as well.
Beware that you are a glass cannon. You will hit very hard with your basic attack as well as your abilities but you are relatively squishy.
Maxing our RMB for the damage and slow and cooldown as you will just be using it off cooldown when fighting. You will win every 1v1 with the exception of Crunch being your biggest counter.