SMITE

"As Achilles get 2 or more executes with a single use of his Fatal Strike Ability."

Achilles Ultimate is Fatal Strike.
After a second or two, you dash forward a short distance, passing through all minions in your path. You will stop at the first god that you hit. If your target is within execute range (has 30% of their health or less), then a yellow helmet insignia, will appear on that god when you're nearby.
If you hit your execute on this god, you are able to reuse your ultimate to try to execute another enemy god. You can do this up to 5 times, if you successfully execute an enemy god with each use.
For this achievement, you need to get 2 or more executes with a single use of his ultimate. you only have a short amount of time after your first execute to line up your second. I had a go at this yesterday before the update, and it is hard to line everything up in time and be able to hit both executes.

I would suggest going for this in Arena, as enemies are more likely to bunch up. If you're lucky, you may also be given Achilles in Assault, making this more viable (single lane and no backing).

As for items, you can try building cooldown reduction items to allow you to use your ult more often (such as Breastplate of Valour), or build more power/penetration to help chip down enemy health before you use your ultimate on them (items like Titan's Bane or Jotunn's Wrath, the latter of which also adds 10% cooldown reduction).

Don't forget that you have a second before you actually dash forward, so enemies could escape if you're not careful.