The “participate in killing [character] 5 times” and Ernest’s “25,000 damage to peacekeepers” lore challenges are not progressing in bot battles.
A friend was not seeing Ambra kills as Alani counting and I had the problem with Ernest. At this point, we’re guessing that none of the challenges that specify a character or faction are working, but have not had time to confirm any others (I’ve seen posts elsewhere saying Ambra kills as Galilea are also not counting, though).
I submitted a ticket via the 2K support site, but thought I’d post here as well to see if anyone can confirm problems with other lore challenges not working in bot battles.
EDIT: Forgot to mention that I play on PC. I do not know if this is a problem on consoles.