First time on this website in a long time. These challenge maps are basically all I do in FE:H now, so I thought I would share what I did in my runs as well. Unfortunately, I have no recording software on my phone so I have to take screenshots as I do it.
Turns out I can't figure out how to upload an image here, at least for now.
For Infernal I ran L!Leif, a dancer, B!Roy, and a galeforce Reginn. Reginn took out the axe knight (after inheriting axebreaker), then its just WoMing and galeforecing to death all the enemies bar the lance unit, who attacks into the dancer positioned there (I used P!Azura). Then Leif takes out that guy and the flier above with a dance as Reginn is repositioned so she can take out the final reinforcement bow cavalier.
For Abyssal, Reginn needed an armoursmasher. I used Reginn (after giving her too much stuff lol), Reinhardt, NY!Micaiah, and Cordelia. Reginn takes out the axe knight again, then Cordelia WoMs down to kill the lance user and the red mage, activating defense smoke on Ullr. Reinhardt WoMs to Cordelia and kills Reginn, then Micaiah WoMs to Cordelia so she can take out the bow cavalier. Finally Reginn kills the cleric. I'm actually really proud of myself for being able to find a one turn solution I could do!
If anyone can help me with adding images for next time (the upcoming limited battle set, I think), I would be very appreciative!