Hades

Requirements: This cannot be done until you've completed at least 1 full clear and have unlocked the Pact of Punishment.

When you beat the final boss once, you'll unlock the Pact of Punishment. This is a list of modifiers or conditions that you can activate for each run, and each has its own level of difficulty added on, represented by "Heat" levels. Some conditions are harder than others, and each one gives you between 1-3 Heat. In addition, you can add multiple levels of each condition, increasing its potency. As the Heat gauge increases, you'll need to combine more and more modifiers to reach the next level. At each new Heat gauge level, new "Bounties" unlock, which essentially just resets the first-time completion rewards for the boss fights (for each weapon), giving you a new way of earning more Titan Bloods, Diamonds, and Ambrosias.

For this trophy, you'll need to complete one full successful clear with 3 levels of the Extreme Measures condition active. This condition changes the boss fight in its respective biome by giving the boss new attacks/techniques. Because this trophy is specifically for completing Elysium with it, 1 level of it will not suffice, as each level is only for 1 of the Underworld biomes. The first level affects Tartarus, the second affects Asphodel, and the third level of it affects Elysium. 

TIP: Even though the Pact unlocks after just 1 clear, I would really suggest waiting to do this until you're further in your game, because this is not an easy boss fight. 

See below for more details on the altered boss fights [SPOILER WARNING]: 

Megaera, Alecto, and Tisiphone:
Rather than just 1, when using Extreme Measures you will have to fight all 3 Fury sisters simultaneously. 1 will be considered the 'main' boss, while the other two support. The support sisters do not take damage, they're just there to make things harder on you by damaging you from all sides! Whoever is the 'main' has the same attacks as normal, while the 2 support sisters will have additional attacks.

Here are the different attacks for each sister when they're the support (credit to the wiki site for the definitions):

Meg Support:

• Support Flame: Megaera summons a large flame circle near Zagreus' current position, dealing 8 damage when it activates if he is inside it.
• Support Volley: Megaera summons a flame pillar which fires a volley of rapid shots around the arena, dealing 4 damage on impact. This ability is only able to be used if the main fury is under 50% max HP.

Alecto Support:

• Support Whip Shot: Alecto summons a Whip Shot which acts the same as it does in her fight, bouncing off walls and doing 7 damage a hit to Zagreus.
• Support Lightning Chase: Alecto repeatedly summons a circle on Zagreus' current position, dealing damage if he stands in one when it activates. This ability is only able to be used if the main fury is under 50% max HP.

Tisiphone Support:

• Support Bombing Run: Tisiphone places lengthy rows of damaging circles along a direction of the arena, which detonate after each other in a row. They deal damage if Zagreus stands in one when it detonates.
• Support Fog: Tisiphone covers parts of the arena with clouds of dark green fog, making it difficult to see enemies or Zagreus in that location for a limited time.

Lennie, the Bone Hydra: 

There are a few big differences in this fight. Firstly, the boss is now in a completely different chamber. It will be a smaller island, split by magma. Rather than being tethered in place at the top, the main boss will be in the center, and when the support heads spawn, they'll spawn on all sides instead. Another big difference is that the boss is no longer stuck in one place for the entirety of the fight. Once he reaches 66% health, the head will break off and now be able to chase you around, trying to lunge at you and slam the ground three times in a row. It will remain this way for the rest of the fight.



Theseus and Asterius:
This fight changes quite a bit, rather than just a few extra attacks or tweaks. It's one of the hardest boss fights in the game, so be warned.

Theseus:

Theseus now appears on a chariot, which does a lot of damage if you run into, and has a much higher health. He will no longer have any of his normal attacks. Instead, he now has 2 new attacks. First, he has a new Cluster Bomb attack where he'll drop bombs all around the arena, both along his own path and throwing them at you. Second, he has a Bullet Lunge attack, where he charges through the center of the arena towards you, spraying bullets in a cone in front of him along the way. Once Theseus reaches 33% Health, the chariot breaks and he regains his normal attacks, beginning in Phase 2 where he calls for his Olympian Aid, summoning a god to help, just like he does in the normal boss fight against him.

Asterius:

For the most part, Asterius keeps his normal moves, but with a few changes. He can now chain Axe combos in quick succession, and same goes for his Leap combos. When he uses a Leap combo or does the overhead axe slam, a shockwave bursts from around him outwards as he lands, similar to his shockwaves in his normal Phase 2, but now in a circular fashion rather than the original line. Lastly, the Bull Rush remains the same, but he runs much faster now.

He does gain 1 new attack, though, in which he rapidly spins his axe around him several times, and has a rather long reach.