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In-Game Award Description: “As Scylla reset your ultimate three or more times in a single use.”

You're definitely going to want to do this in Arena. Build Scylla as all Damage and wait for a team fight. Her Ult does a lot of damage, but they still are gonna have to be pretty low on health.
I believe that it requires you to:
-Activate your Ult (4/Y)
-Get a kill, so that your Ult let's you attack again.
-Then, kill another person with the 2nd attack.

That's how I earned it. I got a kill with the first attack and the second attack. I hit another God with the 3rd attack, but didn't kill him so I don't know if that mattered. The build I used is obviously going to be on screen if anyone wants to use it.
Video of me getting it (and a Penta):
Good luck because it requires some.

(Of course, this was my situation. Results may vary. You may have to kill 3 separate people.)

Requirement:
Yes, I’m a Monster: “As Scylla reset your ultimate three or more times in a single use.”

Explanation:
Scylla’s Ultimate I’m a Monster (4th ability, ) is a powerful ground target attack. If Scylla kills an enemy God with the attack, I’m a Monster resets and allows Scylla to attack again within 6 seconds. You must kill 2 3 enemies individually. You must activate, get first kill, ultimate resets, get second kill, ultimate resets, get 3rd kill. The ultimate resets after the 3rd kill but nothing must be done with it. and the achievement is yours.

Thank you to ImJustYourDaddy and ManicMetalhead for their clarification on the third kill not being needed, only the third reset.

Tips:
I believe this achievement will be earned easiest in Arena; Conquest gives too many routes of escape for the enemy team and you only have 6 seconds to attack after each reset. Make sure to lead your target slightly as there is an animation delay in the attack. At max rank I’m a Monster’s movement speed buff doubles so you will have a greater ability to chase down fleeing enemies. This is a very situation dependent achievement so make sure to build max damage and cooldown to give you the best chance at earning it.

If you have any corrections, tips, or tricks comment and I will be sure to edit/ add them.

To add to other solutions - It seems that you are able to kill a minion with your ultimate, after your second reset, if you are unable to reach/kill a 3rd god and still unlock the achievement.

I've attached a game clip of myself doing this and unlocking the in-game achievement.