Due to public demand I have compiled a pretty spoiler-heavy step-by-step guide to encounter and catch all of the four mythical manamons in Manamon 2: Eternal Requiem. This one is written from memory, some directional instructions will be a little vague. If someone wants to contribute more precise directions I can include them in a later update.
1. The three stone mythicals
What you need:
5 stadium keys
At least one manamon of level 60 or above
One manamon with the water typing or the move "dive" in their known moveset
At least one black matter husk (more about them later)
Black matter goo
Some mananets, preferabely earth nets you can buy in the Brytanburg super store. They seem to yield the highest catch success rate
1.1. The matter with the black matter
You can find three black matter husks and one black matter goo in the world. You need at least one husk and the goo, collecting all three of the husks makes a boss fight much more manageable though.
Places to find the husks:
As loot for a fight against a certain thug you already encountered once. Find him in the swamps east of Elatia City, reachable through a house on its east side via Elatia Walkway. Make your way to the northeast end of the map to a tree you climb. There you find him southwestish. At this point of the game his team shouldn't be a problem, biggest hitter there is a level 65 sansurgeon thats pretty much hardwalled by any steel type.
Hidden in the lower catacombs in Requiem reachable via the northern part of the catacombs antechamber. Those are easily the most annoying area to traverse in the game and I'm totally not sure where down there exactly it is. Someone mentioned it to be on floor 3.
As reward for the coin collecting side quest in Vermechaw City.
There's 3 coins in the power plant, 1 coins each up the tree, in the hotel, in the market, in the eastern house that leads to the valley, and behind one of the buildings somewhere outside.
Place to find the goo:
Find some swimmable water in the northeastern part of Shadow Canyon. There on the upper right corner you can hear a stone door leading into a cave. Its pretty small so don't fear getting lost. Make your way northeastish towards a audible teleporter. Somewhere below and past it is a chest you need if you don't have the move dive naturally. In there you find an equipable item that gives that move to any water type you have.
From there find your way to the northeastern corner of the cave. You hear a gurgling noise - thats your goal. Equip the diving gear to your water type to interact with that deeper part of the water. Dive east through another door and press interact to resurface. There east you find - behind an npc who blocks you if you are to small - yet another deep water patch. Save before interacting, its boss-fight time.
Kill the death cry machine first, after that the spawning machine. If you damage the hyperizer it redirects that damage onto the hyper tarboo. So attack the hyperizer first untill it goes down, only then go for the hyper tarboo itself. It mainly does water and sound damage so if you bring a team that resists that you're pretty much set.
Your reward is the black matter goo lying around somewhere on the ocean floor.
If you have as many husks as you want to collect plus the goo go for the Thunder Prairie out the northern end of Brytanburg North. There in the southwest you find a house behind a swimmable water. In there is a person who crafts one black matter blade for each husk you have.
1.1. The guardian
Only when you have at least one black matter blade proceed here. Go back to Lellapol Village into the cave of fate, you can enter it now. Kill all the sullorbs you hear by bumping into them. If the room is cleared a stone pillar arrives that you climb. Find your way southwestish past a pushable boulder to an ocean of fire. This one is a boat puzzle like the ones in the water stadium. Only catch is: If you miss your timing your first manamon dies. So save and reload until you drop down to the next area without to much losses on your team.
Proceed across another water to the fateful underground. There you hear four boulders with letters (ctrl + interact to read the letter) You have to rearrange them to spell the word FATE.
This one works exactly like the other boulder spelling puzzles you've encountered until now, the only catch is that you can't move them yourself. Instead there are four switches on the ice left of you that, when run into, move the boulders for you.
If you interact with one boulder you hear a high pitched glowing noise. That means that this boulder will be moved around by the switches. Play around a little with the ice, you can reach all four switches, some directly, some via a small rock island in the middle of the ice. Move the boulders around with the switches until they spell out "F A T E" from left to right while touching eachother.
If done correctly you get a cut scene telling that a stone pillar has appeared somewhere else. Find that, it's back up the ladder somewhere below the teleporter that warps you back outside the cave. Equip your three manamons you want to use with the dark matter blades and save once more before climbing.
You'll enter a room full of spikes and moving sullorbs who will throw you out if you touch them. Make your way across it to the right and save often. At the right end you stumble into the next boss fight.
Nothing to big to tell about the guardian besides you need the black matter blades equiped to actually damage it. It's using mostly stone skills so if you resist those it helps. Confusion and something that hits dragon for neutral or super effective damage is also useful. This fight shouldn't be to hard for you by now though. With the killing blow you unlock the catchable forms of the stone mythicals.
It is the easiest to find. Leave Sonasette City through the western exit. Walk the tunnel all the way to its western exit. There you find Brezgard in the southwestern part.
Brezgard is a stone and air type with good physical attack, health and great speed.
Not to hard to find either. In Tradale Village it is on the other side as the stadium in the dragon park, so westish somewhere. Can't miss it.
This one is a stone and dragon type with tank stat layout: great defenses and attack stats on both sides and god awful speed.
This one is a little more tricky. Go to the northwestern end of Mordunt Island and find a swimmable water there. You will hear another gurgling patch of deep water you need to dive through. There do what you've done to find hyper tarboo.
Karugard is a decently defensive and physically hard hitting stone and fighting type with mediocre speed.
1.5. Some general advice to catch all three stone mythicals:
Save before engaging in the battle. If you kill them they're gone for good.
You're probably way overleveled for them by now. If you oneshot them all the time bring a manamon that learns powerfang or soul split to whiddle down their health with no danger of killing them by accident.
Use an earth net, as mentioned before they have the best chance to actually catch the mythical.
What you need:
Complete the story untill the destruction of requiem
Requiem Dust (more on that later)
Ideally a gamma net, hopefully you haven't wasted that one you got during the story. There is another one thats extremely hard to get. Search for Pierre if you want to know more.
2.1. The setup:
Revisit Requiem via the time machine in the northwest of Tradale Village. There you find Andromeda on the second floor of the castle in Requiem Village. Fight her to get a bottle of Requiem Dust.
Some perceptive members of this forum suggested that you have to have beaten the master stadium first for her to appear. So if you haven't done so and can't find her that might be the case. I will update the guide accordingly as soon as we have proof for this.
Now go back to the end of the world past the frozen hinterlands. Approach the cliff at the northern border and use the Requiem Dust there. You're getting teleported back into the caves you've encountered Hathorilian first. Make your way into the shrine as you've done before. You will face another boss battle there.
2.2. Nothing new, only more of it
You will fight four level 60 Hathorilians at once. They will, as the first one did, drop boom boxes after you've damaged them enough. One boom box kills your manamon, the other damages Hathorilian. They alter every time, so if the correct one was the first one last instance it is the second one this time and vice versa. Kill all of the four Clones to reach phase two of the fight where Hathorilian becomes catchable. Use the gamma net, you won't need it for anything else more difficult.
Hathorilian is an awesome mixed attacker with pretty diverse moves. It is earth and air type.
2.3. Some general advice for the fight
It helps a lot if you resist earth and/or air for the fight against the clone Hathies. They're also not immune to paralyze but immune to electricity. So stun bolt doesn't work without a lightning rod, stunning call does however. Confusion can help too.
If damaged enough a clone drops out of combat and leaves the boom boxes behind. So to lessen the damage you take you want to have at least one set of boom boxes on the field at all time. After you destroyed that set the clone in question will stay on the field for one round before able to drop boom boxes again. So focus your attacks on another one instead.
Bring lots of patience or revives because as far as I know the first boom box setup is always random. So more often than not you will whipe out half your team with the wrong choice and need to burn through revives or reloads.