I don't know if this has any wiggle room on the suggested criteria (like damage three Gods with your ultimate/4 at a single time and then kill them afterwards) but I haven't unlocked this yet so I'm pretty much just doing this guide to confirm that you can not unlock this by killing one God three separate times (as may have been the case at one point, at least it was/is on the Xbox version).
In order to most effectively go for this you'll need to counter-productive to how Ymir is usually played. Normally you want to be the first one in the fight but in this case you want your enemies to be slightly weakened.
Use Blink to get in, then use Curse (you'll need to be level 12 to get two Artifacts. Then hit your enemies with 3, 2 and set up a wall so your enemies can't escape with your 1. The ordering of things after Blink can be changed somewhat, it's very situational.
Building magical items would be ideal as most people will try to run away once you start your ultimate so defense won't be necessary for this achievement but maybe notify your team that you won't be building tanky items. Although to still maintain your God role somewhat maybe a tanky/magical hybrid build would be best.
Don't forget that you can cancel your ultimate at any point in the charge to cash in on the damage built up if you're afraid a enemy might escape, it just might be enough to kill everyone.
You can do this in any mode with a minimum of three enemies which is all the normal default modes; Arena, Conquest, Joust, Clash, Assault (you'll need to get lucky and get Ymir from the start, a re-roll or a trade) and lastly Siege.
Most Match of the Day (MOTD) will have 3+ team events but sometimes you won't get to pick your God and some days it may be a 2v2 or 1v1 special match. Some MOTD's can hep you in giving you maximum reduced cooldowns from the start or a lot of gold so you can have a completed build but this works against you too as opponents that have escape abilities/attacks can get away more times and your opponents may be able to withstand your ultimate with their completed item builds.