You can clear out the lower section first, but watch out for the 2 Red Bombs (1 on each side).
After clearing the lower area, run up the stairs and jump off onto either side.
There is a Skeleton at the very top on each side and about 5 more on the mid-level on each side.
You can only use elemental crystals or magic to defeat Skeletons.
Considering how many there are, an elemental crystal is the preferred method.
Without an elemental crystal, you'd have to milk magic stones from the Skeletons, which can take some time.
The Hurricane Crystal works exceptionally well against Skeletons.
After you clear out the stage, a King Red Bomb will make an appearance.
This mini-boss will launch flames that sort of lock on to you.
You can attack this mini-boss with your sword to weaken it, but magic should be used to defeat it in order to avoid the explosion damage.
Once you take it down, proceed up the stairs for the third (at least) time to the next area.