Easy solo as BST: Run to G-9 on second map, charm an Oil Slick and 2hr. Head to E-11 and attack the BST's pet. It won't aggro other Fomors, but the pet will link nearby bats, so watchout.
Kill the pet first, and you're good for the fight. Wait 14 minutes for BST respawn if you didn't get drop the first time (will spawn w/o pet this time), and try again.
By now, your time is up with the oil slick, so Leave it and try again in 2 hours if you didn't get it. Might as well farm so fomor codexes back at the big room on the first map, while you're at it.
Great to keep downtime minimal for BST which means more chains. Good for /WHM and /NIN (at later levels when using Rune Axes).
Like Ostrider said, need to complete Brygid's quests for this.
A little elaboration to Ostrider's comment... Keep in mind that there are a few more steps than just trading the subligar and once you ask to quest a certain subligar. You must have and be able to equip a piece of AF(any). You cannot do any others until that one is completed(she will ask which one you want beforehand). This means get the subligar before you start the quest!
The hardest part is charming the oil slick, really... make sure you have a Reraise earring or something before attempting, because you can struggle with the charm even in the best CHR gear available.
@Anethesia: He's right about that, but wrong about the latent activation.