There are a lot of new mechanisms in Fontaine that you might not remember all of them for now. And with how many Tutorials there are from version 1.0 to 4.0, it will be a hassle to scroll and find the specific tutorial you want to see. So here’s a handbook on almost all important things/solutions for puzzle in Fontaine that you need.

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Underwater Puzzles

Dolphin Dive

This is an unimportant mechanism but since only certain characters can do it, I’ll include it here. By pressing [Space] on PC, your character will swim upwards, and when almost at surface, the animation differs for certain group. If your active character is anyone from Fontaine or Hydro Traveler, they will do a Dolphin Dive before entering the water back.
But if your active characters are anyone aside from Fontaine and Traveler, they will boringly pop their head up above the water slowly.

Fontaine’s Blessing

You will get the blessing of the Transoceanic Fontemer Waters once you interact with a Statue of the Seven in Fontaine. Under the protection of the Transoceanic waters, what you expend while moving underwater is not Stamina but “Underwater Stamina.” That means when your Underwater Stamina is expended, you will not drown. This effect is only available in Fontaine’s underwater area and not other regions.

The Prism in Elynas

This Prism and Ore will only be available in Elynas’ body (in underwater Merusea Village during Ancient Colors quest). You can attack the Prism (Melee characters are best for this job) to release energy in the corresponding direction, which can resonate and destroy the Ores.

But, some Prisms will exist in an inactive state (you can look by their brightness, if its glowing bright: active, if not glowing: inactive), and will only be activated after receiving power unleashed by other Prisms. It’s the same method as before where you just need to attack the activated Prism, but you need to aim it to the inactivated Prism.

Echoing Conch

This conch can be seen in both surface and underwater, but mostly in underwater. By activating this Echoing Conch, it will generates a visible sound waves that detect hidden/invisible objects nearby (you can tell by the blue glow). Those ‘invisibles objects’ can be Ousia/Pneumia Blocks, Storage Box, etc.

Abilities of the Transoceanic Fontemer Waters and Heterochromatic Creatures

These Transoceanic Fontemer Waters (TFW) will appear beside you when you dive underwater by clicking [Right-Click Mouse] for PC, allowing you to deliver attacks but does very little damage and not recommended when fighting underwater enemies. The main effect of this TFW is to attack special Heterochromatic Fontemer Aberrants and absorb their power.

Heterochromatic Hunter’s Ray’s Ability

Released Fontemer Water Blades that are long and sharp. Hold to aim and release. With this ability, you can cut through the weak links of Fontemer Seagrass. Deals high damage to underwater enemies.

Weak links with some endurance will sometimes emit a special blinking light. You will need to cut all the available links simultaneously with Fontemer Water Blades in such cases. To do this, you need to position your character at the best spot and unleash the Water Blade at an angle that can cut all the weak links at the same time.

Heterochromatic Blubberbeast’s Ability

A pulsing sonar wave that has detection-based capabilities. Holding it down will allow you to aim while continuously releasing sound waves. These sound waves can help explode underwater Exploding Barrels. Deals decent damage to underwater enemies.

Heterochromatic Armored Crab’s Ability

Creates a heavily armored shield capable of releasing shockwaves that can shatter stones.
Holding it down will continuously expand the shield, and when you release the skill, this will release a shockwave in the direction you are aiming at. If you are attacked during this time, it will unleash an even stronger energy bolt. In other words:
– Tap E to create a shield
– Hold E to continuously expand the shield, then release to unleash a shockwave that can destroy breakable wall underwater
– If you’re attacked when expanding the shield, the shockwave will be even stronger and can destroy Bullet Barnacles.

Bullet Barnacles

A dangerous underwater life form that can fire energy bolts at nearby characters. Holding down the Armored Shield can allow it to absorb attacks and release them as energy bolts, giving your attackers a taste of their own medicine. Remember, expand the shield and absorb the attacks first before releasing to unleash a stronger shockwave (a normal shockwave can’t destroy it).

Narcissus’s Evil Bubble Formations!

Can only be seen in Annapausis during The Narzissenkreuz Adventure quest. A defensive device that can lock on and fire Mist Bubbles at those brave enough to enter its targeting range!
Use condensed waterplanks (by activating the Crystal Mechanism) to block the Mist Bubble attack and use the said terrain to approach and extract the Hydrogranum that allows it to operate to shut it down.

Fantastical Floating Ball

For this puzzle, you need to allow high pressure water currents from nearby Water Vent to be aimed at these spheres. Then, the Floating Ball will move following the water currents toward the Ringed device and activate it. That’s how you solve the puzzle.

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Surface Puzzles

Pneumousia Relay

This is the most common puzzle in Fontaine so you need to understand how it works and get familiar with it. As you can see in the images above, a Pneumousia Relay has 3 states: Ousia (dark purple), Balanced (green), and Pneuma (yellow), and these states can be altered when attacked by their opposite.

In other words, attacking Ousia Relay with Pneuma Blocks (that can be found around the relay) or any Fontaine characters with their respective Arkhe, will turn it to Balanced. Here’s the Razor language: Ousia + Pneuma = Balanced state. And vice-versa. All Pneumousia Relay puzzles usually want you to revert them to Balanced state (Keyword on ‘usually’).

Pneumousia Block

This is the Pneumousia Block I mentioned before. These Energy blocks are separated into Pneuma Blocks and Ousia Blocks. After collecting an energy block, your next Normal, Charged, or Plunging Attack will, upon hit, release the energy stored within them. Once again, you can also directly use Fontaine character’s attacks with their respective Arkhe to complete Relay Puzzles withouth using Pneumousia Block.

Pneumousia Storage Box

The Pneumousia Block from before also can be used to open this Storage Box. First, look at the color to figure out whether it’s Ousia or Pneuma, then take the opposite Energy Block (that will definitely be near the area) and attack the Storage Box to open it.

Enhanced Pneumousia Amplifier

A mechanism that can buff nearest opponents. Similar to other Pneumousia mechanism, you can shut it down by attacking it with Energy Blocks opposite of what the Amplifier has.

The Miraculous Antoine Roger Aircraft!

This is an experimental Aircraft that is propelled by mutually annihilating Pneumousia energy. For example, if the Steering Wheel on the Aircraft glows with Ousia color, you need to use nearby Pneuma Orbs and hit the Steering Wheel so it will turn to Neutral. Remember that: Ousia + Pneuma = Neutral state. 
You can fly on it to the pre-set route upon being activated (you can’t change the route). During the journey on the aircraft, it will sometimes stop because of some mishaps like Anemo Slimes floating above the aircraft, so you need to clear them out to make the aircraft moving again.

If the Aircraft isn’t on the platform at its original position, you can interact with the mechanism in the image above to summon the Aircraft back.

Beastly Rift

Wow such purple grass, what is this? This is some kind of fantastical arcane formation left by someone It’s a challenge. It will summon monsters from another world that will try to break the crystal restraining the formation. You must defeat all attacking monsters while ensuring the crystal stays intact to complete the challenge and get your rewards.

Miraculous Hydrograna

After you collect three Hydrograna (the left image), they will combine into a Hydro Core (the right image) that will continuously apply Hydro to the surrounding environment like Barbara and Nilou’s Skill. This Hydro Core usually are used to complete Water Volume Detection Crystal puzzles below.

Even if you have not yet collected three of them, your active characters can cause Hydrograna to grow into a Hydro Core if continuously affected by Hydro (being wet with Barbara’s Skill or dip your feet in the water to get the Wet status).

Water Volume Detection Crystals

Usually, there will be more than 1 Water Volume Detection Crystal (WVDC) in one area. You need to activate all of them at the same time by using Hydro Core (or cheat by placing Kokomi’s Skill near the WVDC). Anything that can make them Wet is counted as activating the mechanism.

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Enemies

Icewind Suite: Coppelia & Coppelius

First of all, you need to know that Coppelia and Coppelius drops different kind of materials. That’s why make sure you choose correctly when talking to Maillardet. How to choose? Talk to Maillardet in front of a Kamera near the Icewind Suit arena.
Coppelius dropped the Pneuma component (white one)
Coppelia dropped the Ousia component (dark purple-ish one)

For Coppelia, she will stop at the center of the dance floor and expose her spare clockwork component charged with Ousia, increasing the efficiency of her exertions and summoning countless whirlwinds. 
During this phase, using Pneuma-imbued attacks will reduce her offensive capabilities (not completely paralyze her). How to know whether Coppelia has been attacked with Pneuma? Listen to the sound effect, you can hear something like glass shattering. Characters with Pneuma: Lyney.

For Coppelius, he will stop at the center of the dance floor and expose his spare clockwork component charged with Pneuma, increasing the efficiency of his exertions, granting him a shield, and generating three retributive Frosthearts. 
During this phase, ignore the Frosthearts and focus on using Ousia-imbued attacks to break his shield. Characters with Ousia: Lynette.

Mek (Mecha?)

Mek are all the machines in Fontaine that have either Ousia/Pneuma in their cores. Similar to Icewind Suite bosses, if you hit their core with attacks imbued with Ousia/Pneuma (opposite on what they have), it will cause them to overload and get paralyzed. How to know whether they have Ousia or Pneuma energy? Just look at their mechanical body and you can spot either purple or white color on certain body parts (different part for different Mek).

Emperor of Fire and Iron

An Armored Crablord with twin molten horns located high up on its body that are Pyro-aligned organs that can unleash more vicious elemental attacks and grant it even stronger defensive capabilities. If you use Elemental Reactions (Hydro is the best, obviously) to remove its Elemental Shield at a suitable time, you can weaken it for a certain period before it can create another shield. 
The ‘suitable time’ is when it ducked its body down a little to attack you, or using characters that have Skill/Ultimate that attacks from above (like Ayato’s Burst).

Aquatic Life Form

Currently in 4.0, there are 3 hostile Aquatic Life Forms: Sternshield Crab (Pyro), Bubbler Seahorse (Electro), and Archangel Sea Hare (Cryo). Each life forms have their respective Elemental Shields. Similar to Emperor of Fire and Iron, under the effects of their Elemental Shields, they can unleash fiercer elemental attacks and possesses even stronger defensive capabilities. That’s why it’s recommended if you use Elemental Reactions to remove the Elemental Shield first.

Breacher Primus

There are a few types of Breacher Primus, some of them: Shatterstone (Geo) and Overgrown (Dendro).
For any Breacher Primus, it will enter a stressed state and unleash a Stonefall (for Shatterstone) / Lushmissile (Overgrown) attack while under the protection of a Geo/Dendro shield. You can remove this shield by using Elemental Reactions or attacks imbued with Ousia and Pneuma. If the shield is broken during this period, it will fall into a paralyzed state.