After having obtained the 4 Weapon fragments, bring them to Arazlam's House (southwest of Hillsdale) so that he can craft you something nice.
The 4 (mostly optional) Weapon bosses can be found at these locations (in order of - possible - appearance):
- Esto Yensa (central outside door, only after having completed the dungeon) - this is the only Weapon boss that can already be encountered in the game's first part.
- Ancient Cave/Castle, somewhere on the castle's second floor
- Tower of Babil (mandatory story boss)
- Moon (on the plateau area north of Starlight Ridge)