There are also DRK type skeletons, so 3 types. The wyverns are also undead, so can't be drained or aspired and resist sleep. I recommend killing the wyverns first.
This is a pretty simple 'zerg' type Assault. There are 2 types of Skeletons, BLM & DRG. Its good to have a MNK or PUP for the skeletons, and Silence is definitely a big help for both the skeletons and ghosts.
Both Skeletons will do a TP move called 'Black Cloud'. It is an AOE drain move more powerful than Blood Saber, did about 200-400 drained dmg to everyone within the radius. Pull the skeletons to a safe area,and keep mages in back, they aggro to Low HP & Sound but don't link. Fighting 2 skeletons at once and having them both 'Black Cloud' could definitely lead to a wipe.
The 2 times I went, the monsters were in the same locations. If not, I apologize for the misdirection.
Directions: From the starting point, head south then east. There will be 2 skeletons in each storage rooms(2-3), and a few walking about. Kill them all in this dead-end section and head back to starting point. Head north from that point until you see 2 doomed in an open area. Kill them and head West/North into a tunnel, kill all monsters in this other dead-end section and that should unlock the rune. The Rune appears back at the starting point.