Progress does count towards PvE (against the AI)
From what I've seen, working as some high damage specialists or strikers seems to be the best bet for kills.
Aisha, Ignitia, or Turner with base loadouts seem to do relatively decent at gathering kills.
Tooth and Tops in the bruiser category is my personal favorite and I can average 15-20 kills (in most) games against the AI with just the basic loadouts.
Move with a teammate or two and try to single out weaker or hurt Hyper's while spamming minions to try and out level.
It's grindy, but this is a grindy game and hopefully you can do decent against the AI.