I can't remember the ranges for all of these, but I did most of them fairly easy as level 62 BLM rabbit in Monstrosity. A little time in Ghelsba Outpost and Valkurm Dunes was sufficient. I haven't had as much luck with the highest tier, the 1110 - 1120 objective. In about 4 hours I managed to get one objective done.
My rabbit can't really put out that much damage unless I use ancient magic, and I can't seem to hit the sweet spot with that. I've tried on my regular BLM (skeletons near gate #3 in Garlaige Citadel) but I keep getting close but no cigar. I'm using Baqil Staff and some lower tier (1-3) single target nukes.
I tried on some melee jobs. I got 1 target Fell Cleaving frogs in Abyssea - La Theine. But my WAR is poorly geared and not particularly durable so I got killed after about 15 minutes. I tried Chi Blasting as MNK, but Chi Blast damage is all over the place. I tried going as MNK and pounding pots in Abyssea - Grauberg. I get a lot of 1000+ damage per fist on criticals, which are frequent, but it's always around 1050-1100. I can't seem to get it down to that 1010-1020 range.
Has anyone had any luck with this one? BLM damage seems the most consistent, but I don't know enough about how the damage from nukes is calculated to zero in on that narrow 10 point range. I'm thinking my next attempt is to level up my rabbit some more and maybe try some different instincts.