You can get the Core Cooling Achievement by cooling off the boiling pond of water found in the Beryl Region in Fontaine, south of the Statue of the Seven.
First Puzzle: Water Volume Detection Crystals
There are three Water Volume Detection Crystals around the pond, and you must move them all to the center before activating them.
Move the Crystals
The First Water Volume Detection Crystal is hidden inside a Pneuma Storage Box, so you have to attack it with Ousia, either by attacking with Linette's Elemental Skill or absorbing the Ousia Block nearby.
The second Crystal is trapped behind some vines, so you need to burn them either by using a Pyro character or spreading the fire from the flowers next to it.
Enemies surround the third one; kill them, and the Water Volume Detection Crystal will unlock itself.
Activate the Crystals
If you don't want to swim in boiling water, glide from a higher place to the center.
To activate the Water Volume Detection Crystals, you have to constantly apply Hydro to all of them, grab the Hydrogranum, and either use a Hydro character that applies your team with Hydro or by stepping into the boiling water.
Second Puzzle: Extinguish the Torches
Finishing the first Puzzle will take you to the second one, kill all the enemies so they don't bother.
The torches will light themselves up whenever you turn them off; you must put Hydro cores on the pedestals next to each torch.
To create a Hydro core, you have to pick three Hydrograna or pick one and wet your character.
The corresponding Hydrograna for each torch will be nearby; some are inside boxes, and others are inside explosive barrels. If they were exposed, you might have destroyed their hiding spot during the fight.
Now apply Hydro on the Monument and leave; you'll get the achievement when you get close to the pond.
Optional: Kill the Iron Viscount
After the final step, the cave will be filled with water, and some creatures will appear; among them is the Iron Viscount; defeating it for the first time will get you the achievement "Iron Viscount".
To defeat the Iron Viscount, you must return its attacks by holding the Armored Shield Ability, which you can absorb from the Xenochromatic Armored Crabs that spawn with it.
