What's the best strategy for farming this?
Just kill all the NMs you encounter and that's it?
depends if you're purely solo or have a lamp ***. I run w/ only 1 char, the way I approach it is set the cap @60 and do big jumps unless I land 1-2 away from 20/40, then I'll just jump 1 floor with the intent of hitting 20/40/60 for the +2 boxes, and the chances for a purse from the boss on top of the boxes.
On the climb, yes I'll kill every NM I do see but won't go out of my way hunting them on a floor I clear the objective quickly.
I know some ppl who set the cap @20 and just go 1 floor at a time, others who go w/ a lamp *** and set it at 100. It all boils down to what fits your playstyle/aggressiveness.
I don't have a spelled-up/geared-up BLU, so I take my BLM. Most everything outside of NMs and flayers dies to one AoE nuke, and the Claustrum all of a sudden makes sense w/ its wonderful aftermath ;)