Summary:

- Fir Bholgs, least the Humes, are easy for a BLM to solo.  They're SAMs, easily gravitied, cannot be bound (I never got it to land), but can be slept.  Since I'm hume those are the mobs I had to kill to pop the chests and vortex.
- The real problem here and a very consuming time eater is dealing with links.  When they linked I was pretty much dead, but I learned a thing or two when trying to pull.
- I died twice doing this.  I had to two-hour to save time.
- I opened the chest with 5 seconds left.

Edit:

The mobs in question are Fomors.  They have slightly over 4k HP, similar to that of Ebony Puddings, but without the damage bonus.  It takes a few good nukes to kill these.  I went Thunder IV > Fire IV > Thunder IV > Fire IV > Thunder III to kill the first one, as fomors don't like ice spells.  On the second one my two-hour was up, so I did Thunder IV > Burst II > Thundaga III > (two hour wore off here) Thunder IV and easily killed it.



As one can see here, I had a few mobs on me at the end but due to the time I had left I made it out alive.  I had just opened the chest at that point.  If I wasn't so low on time I would've ended up dead from the last 
'link'.

Next time around if I can get the mobs down very fast I can give the second floor a try but due to links getting to the second floor is a "maybe".  There's times like this that I'm glad I'm Hume - Tarutaru fomors (BLMs) here have very high magic defense, as well as the Mithra fomors (RDMs).  As I still do limbus with a black mage team in Arisen, this is a thing I'm doing on the side for a sooner chance at getting AF+1.