I tried to kill one using a Shark Gun and Iron Bullets as NIN/DNC yesterday. But it depopped still very much alive before I was able to get it to 30%.
I went back as NIN/RNG later and was able to solo one. Get 150%+ TP, pop sushi, Sharpshot, Slug Shot, Barrage, shoot, Slug Shot, shoot a bit more, kill! Of course a real Ranger would probably be able to drop it with just a Slug Shot and Barrage, but it's a nice alternative for people too lazy to actually level it (still 57!).
The Shantotto expansion has been (in my opinion fairly) criticized for the artificial difficulty of NMs that only take certain types of damage. There's also the whole synthing + critical breaks thing for people who don't have crafts leveled (as well as some from people who do).
Ninja is in an odd position with the NMs in that it can deal slashing (durr, katanas), piercing (dagger), ranged (gun), and blunt damage (h2h and preferably some Waghs, Warp Cudgel is too low DPS), AND magic damage (-ton Ninjutsu). With the exception of magic damage NMs, which I killed with a bunch of people from Epic, I was able to solo all the NMs. I think I'd probably need to unlock the three :San spells that work on the particular NMs and go /RDM with HQ Staves to drop them in time. With just some INT/MAB gear it wasn't enough.
It's still a needlessly irritating and frankly stupid "quest" though. Also, sticking ranged damage-only NMs at the entrance to Ro'Maeve pretty well fucks up the Fields of Valor soloing there for most jobs. I can only imagine the fun that will be camping Shikigami Weapon with NMs you can't sleep, damage, or kill all over the place.
After wandering around the sewers under Windy collecting glowy things I'm now up to a BCNM with a bunch of Tarutaru Fomor things. If you haven't done this expansion, I assure you that no it really doesn't make any more sense in context.
After that it's some cutscenes, collecting more glowying things in a different crappy hole in the ground, and then a fight that most people are saying is ridiculously hard.