After beating Providence's first phase he will summon two worms; each with their own health bar.
The red Gilded Wurm will fire a laser at a target that follows you and deals high damage/hits rapidly; this should be avoided no matter what. The blue Gilded Wurm fires 3 lines of 5 projectiles that are easy to jump through.
Like the Magma Worm these have multiple segments to them, so any item or skill that hits multiple targets will make short work of them.
The monster log dropped from the worms is labeled as "Ornate Wurm". They do not, however, appear in the actual monster log, although they do count as the entry for the Magma Worm. "Ornate Wurm" also appears on the death screen if you are killed by them.
The worms are partially immune to the effects of the Unstable Watch. They will continue to target the area of the screen the player stood in when they used the watch, and will not retarget until the effect ends, but they will continue to move and fire. The Blue Wurm can still deal damage this way, but the Red will not.
Using the Glowing Meteorite will deal massive damage to the worms, usually killing them in one use and rendering this part of the fight much easier but it might cost you some health so using it on low health is not a smart idea unless you are very mobile.
A suggested tactic would be to focus your fire on the red gilded wurm first, as its laser is the bigger threat of the two.