Vampire Survivors

First, you'll need to obtain all standard relics in the game to unlock the stage The Eudaimonia Machine. Refer to The Eudaimonia Machine (5G) for doing so.

Once you have all the relics needed and unlock that achievement, The Eudaimonia Machine appears at the top of the stage list. Pick any character, start it, and head up and into the black blob. After some fast dialogue, you'll be presented with two options.
 

• Too Easy - Unlocks Gracia's Mirror relic (unlocking Gracia's Mirror (10G)) and Inverse Mode
• Too Hard - Unlocks Seventh Trumpet relic (unlocking Seventh Trumpet (10G)) and Endless Mode

Make one choice, and you'll get your relic and its achievement, plus the new mode. To get this stage to show up again from the level select screen, you need to play any stage with the new mode you unlocked. So, if you chose Too Easy and unlocked Inverse mode, start up any stage and turn on Inverse mode. Now feel free to quit out. Back at the level select screen, The Eudaimonia Machine stage will be back at the top of the list. Pick it, head up to the black blob, and choose the other option to unlock the other relic, its achievement, and the other game mode. Repeat the same process agian, starting any stage with the second game mode you unlocked (feeling free to quit out as soon as it starts if you want), and now The Eudaimonia Machine will be back on the stage select screen for the third and final time.

This time, when you go into The Eudaimonia Machine and walk up into the black blob, you will fight the true final boss of the game, the Directer [sic]. During this boss fight, no chests drop, so you won't be able to evolve any weapons. You will fight regular enemies though, so you will be able to level up. You therefore want to play as a character with a good starting weapon, and only choose weapons that are appropriate and still good without being evolved. The fight is described below in more detail.

The first, and most important, thing to mention about this fight is that there are multiple scripted instances of White Death showing up to kill you. Don't worry - these are meant to happen, and you don't need to have revives saved up to get through them. You can't do anything about them. They're just there to sort of troll you.

Throughout the entire boss fight, the Directer is on your left, locked in a set distance from you no matter where you move, and moves back and forth closer and further from you. As a result, you'll need weapons that shoot to the left. There are relics that will be swirling around the boss's head, and those are what you need to shoot to defeat it. Therefore, many weapons will be pretty useless here, such as the King Bible, Song of Mana, Shadow Pinion, Whip, etc. In my opinion, the best characters for this fight are Leda, Red Death, or Pugnala. Leda starts with the upgraded Magic Wand (and therefore automatically targets the relics above the boss), Red Death starts with the upgraded Axes (and therefore shoots scythes in a pattern good for hitting the relics), and Pugnala starts with both guns that shoot out at diagonals. They are by no means required, so feel free to use anyone else, but here is how to unlock each.
 

• Leda is the best by far for this fight, and if you haven't unlocked her (there are no achievements tied to her), she's actually pretty easy to unlock: in Gallo Tower, head south very far, way past the the Metaglio and Ring items on the map, until the outside of the map starts getting dark. You'll eventually find a round, balloon-like boss enemy to fight. I use the word "boss" loosely here, as not only did she not attack me, she didn't even chase after me like other bosses do. She did have a ton of health though, so be prepared to sit there for a while until she disappears, at which point you'll unlock her after the run
• Red Death is another good choice. This character is unlocked by, unsurprisingly, defeating Red Death at the 30 minute mark on any stage. The only way to do this is to have the Infinite Corridor and Crimson Shroud at the same time when Red Death shows up. Refer to Candybox (5G) for getting them. Then, you just need to hang out around Red Death until it dies, at which point you'll unlock this character. Easier said than done though, as it can be stressful to do this for the first time

Whoever you play as, you can't avoid the boss and can't change your alignment to get a better angle, so you're essentially going to be hitting the boss incidentally throughout the fight. Instead, focus on the regular enemies, especially for the first few minutes of the fight, so you avoid them and kill as many as possible to level up. In terms of priorities when you level up:
 

• I highly recommend getting the Laurel, if possible. It doesn't pop up often in general, but it can really help cut down on damage you take, especially during the phase where the columns and rows are shooting out quickly.
• Spinach will really help cut down the length of this fight, because it can really drag on otherwise, especially depending on which character and weapons you have
• Tome will also make it way easier to get rid of the enemies coming through, allowing you to level up more
• Spellbinder increases area of effect, making it way easier to actually hit the boss
• Duplicator is a significant help to any weapon(s) you have, and should be a go-to on every run

There isn't a whole lot else to mention with this fight, as you're essentially going to spend the fight dodging enemies and the columns and rows of damage that pop up in the later phase. You won't have much control over hitting the boss, so you'll just have to let that happen and stick to dodging. Hopefully, if all goes well, after a few minutes you'll finally beat this boss. The fireworks will then trigger and this achievement will unlock.