After you've completed 99 missions (including the postgame-only ones), you can unlock the 100th: Final Test. As the name implies, this is the single hardest fight in the game, and your opponent is... Aleph itself! As it explains, the Commander wants to examine your combat skills, but she's rather busy at the moment, so she sent it to assess you.
And, well, let's just say there's a reason this fight is the last mission. If you can't clear the Holy Host for mission 99, you're not going to stand a chance.
The good news is that Aleph has no resistances. The bad news is that it has no weaknesses. So bring whatever element you want: space, quantum, kinetic, any kind of weapon. Do note that Aleph is fast, so light weapons are generally better since you're in animation lock less.
Aleph's basic attacks are null-elemental and hit pretty hard, but they're 'only' damage. Evade if you can; blocking risks getting set up for something else. The special attacks are the real nasty bit, and boy does it have a lot. These attacks also gain 'variations' when Aleph becomes Void Aleph (see below).
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Iterative Strike: Kinetic. Dashes through you, dealing damage afterwards. However, the first dash can also be a "fakeout" where it will teleport back and restart. Void Aleph can do two or even three fakeouts.
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Laser Sweep: Kinetic. A line AoE that goes all the way to the edge of the arena. Can't be blocked, must dodge. Note that the laser itself doesn't actually deal damage. Void Aleph can summon a portal that the laser will come through instead, though it will always be somewhere you can see.
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Hyperdrive Strike: Space. Aleph starts charging in place. When you see it turn blue and 'ghostly', block immediately; it will instantly teleport to you and attack. This cannot be evaded. You can hit it out of it if you can get there in time, but it tends to only use this when you're far away, so that's risky. Void Aleph will start randomly delaying the attack.
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Core Collapse: Space. Drops a "black hole" mine on the arena. Step in it and you'll be trapped for a few seconds, taking damage all the while, and then easily setup for its next attack. Void Aleph drops two at a time.
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Imaginary Strike: Quantum. This looks like an Iterating Strike, but it will have a blue 'aura' around it. You have to get hit by this so you don't take damage. Yes, really. If you block or evade, you take damage. This can fakeout, though the aura will be present even during the fake strikes... except in Void mode, where only the final strike will have an aura.
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Creation Operator: Quantum. Six copies of Aleph will appear. You have a bit less than two seconds to identify the "real" one by looking for the one that isn't half transparent and hit it out of the attack. If you don't, they will all hit you and deal unblockable, unavoidable damage. Void Aleph will summon eight copies instead.
Once it hits 30% HP, you get the obligatory "now you'll see my real power" cutscene. It puts on a mask, its name changes to Void Aleph, and its attacks are faster; some even have extra properties (see above). Oh, and it has a chance to straight up dodge any of your attacks and counter with an Iterative Strike or an Imaginary Strike; heavy weapons like the Dedekind Cutter literally will not have enough time to react, so switch to a lighter weapon for this part. I guess this is how all the enemies you hit with your Riposte feel.
Oh, and about that 10-minute timer you probably noticed? If you haven't beaten Aleph by then, it will tell you it's bored, and that it expected better. It then performs an Iterative Strike and an Imaginary Strike at the same time; you can't avoid both, and whichever one connect will one-shot you regardless of your HP, defense, or anything. So... don't let it get bored.
Your reward for clearing the hardest fight in the game, besides the "Aleph Null" achievement? A copy of its sword, Durandal. It has the highest DPS in the game and is always treated as if it's superior-element to its target. Of course, it's not like you really need it for anything at this point.