Well, I've only completed two of the maps so far. I think I'm going to wait until Justice server stops LCMing me before I do the third one.
Anyhow, my Brute is:
Electric / Fire Aura / Mu, 1+ billion build, using inspirations that drop
Although I have a 1+ billion build, I don't consider it essential for the build. For reference, my more relevant combat stats are roughly:
Smashing/Lethal: 51% resistance, 13.5% defense
Fire: 90% resistance, 11% defense
Energy: 35% resistance, 12% defense
Ranged: 13.5% defense
Max HP: 1800
Accuracy Bonus: 1.89x
Damage Bonus: 7%
Recharge Bonus: 60% (not counting hasten)
Most of the money in my build goes towards purples that I don't feel I really need, but they provide a nice recharge and accuracy bonus. I don't have any interesting procs (3 damage procs). I farm with this brute fairly often on a map with lots of fire-heavy attacks, and I have PLed people on it before (fewer inspirations drop, but on the fire heavy map I really don't need any insps to keep going). Oh, side note: I haven't respecced for a while... I do have burn (I used to combo it with immobilizations) but don't have Fiery Embrace. I haven't really looked into the new Fiery Embrace, so I don't really know if it's better to have, just noting that I don't have it.
So, map 1 (Nemesis) I think I did ok. I cleared the map with 11m46s to spare. I think I could probably do a bit better if I cared to though.
On map 2 (Rikti) I had some trouble. I only cleared about 90% of the map before time ran out. Part of this was frequent LCMing (I'm surprised I didn't die) and part was probably that I'm unfamiliar with the best way of farming these guys. The rikti are annoying. A lot of them will never run into melee, so you pretty much have to herd them (I went through several spawns before figuring that out) and frequently I would have ranged runners. Also, there are several locations on the map which are poor for herding. To get a spawn to a hard corner I would sometimes have to pull them quite a ways.
I'll give map 3 (Freakshow) a whirl at some point when the server likes me more.
Edit: I did map 3 (Freakshow) with about 13m30s left on the clock, barring a few rezzers and runners that weren't worth chasing down.