Search the aquaducts every now and then for bst. If you see one or two down there ask if they mind helping you. I'm personally down there a couple times a month for NM's with a duo partner and helping various ls members get thru missions and/or subligar. The nin is a solo fomor, she's pretty easy to take out with a 2hr'd oil spill, even easier with 2 and a fun fight with just a dc gloop. Any bst worth his weight can navigate down there easily with no probs. Personally anytime i'm down there with a normal pt or alliance for the mission, I make everyone stay at entrance and just go agro the Minataur myself for the drawin. As one of the other posters stated, alot of norm people will run around down there and cause alot of probs, keep your hp above yellow, and dont play around the stego's, they like to smack you around.
Also, btw, the jse isnt equipable till lvl 50, and to get the quest even started, you need to have a piece of AF gear on. I'm not sure if NIN is your highest or just your current, but any job's af (not weapon) can be used to trigger the quest. Good luck.