First trigger in the battle log was from Slimefoot’s black activated gem (note the 2 damage and life gain). It also gave -2/-2 to a 0/2 Putrid Imp, which killed it (note that is not recorded).
This did not result in the kill objective counting on the Urborg node of AWR.
I took the time to document and report this bug midgame - which caused the app to crash.
So that’s awesome. 
I’ve been in discussion about this topic with my team and can corroborate the claim made above by @jtwood.
I ran with Vraska and used her 3rd ability as a way to kill enemy critters. I also had a Vona’s Hunger, charged in my hand just in case but didn’t have the opportunity to use it.
I killed 4 enemies with Vraska’s 3rd ability and got 0 points for the objective.
Discovering this got the creative juices flowing. I hadn’t attempted 1.3 yet so instead of going with the usual Goblin Fodder build, I went with Bolas II and used Languish to destroy my own creatures and Gharna the Bloodflame to recast them from the yard. Destroying your own creatures with Languish did not yield me any points for the “Lose 3 or more Creatures” objective. This is why I chose Bolas II, I was able to spam his 4th ability to kill my own critters and meet the objective, but I shouldn’t have had to.
I’m willing to bet that -x/-x reducing a critter to 0 toughness no longer triggers whatever event is needed for a “kill”.
It’s not an exile because the critters end up in the yard, so maybe it’s just a creative bug to inspire more creative deck building? If so, I’m good with that, but the objective text should read “Lose X or more creatures by damage taken” or some flavour of that.
This is the same issue that has been reported a couple times with Squee and other Events with “Kill” objectives.
Somehow killing a creature with any -X/-X effect does not register as a kill.
@Tombstone @Brigby was this one of the fixes in 3.3? Its kind of a big deal
I can confirm counters don’t count as the black dino with his -6/-6 does nothing for obj.
Thank you all for the reports. I’ll relay this information to the team for investigation.