The requirements are actually quite simple: Simply finish Story Mode without using continues. Don't worry, you can try as many times as you need to defeat the hidden boss.

(Although there is a hidden achievement for defeating him on your first try)

The boss is quite difficult since unlike any other character, he has EX special moves for free, has a full screen super move that takes half the player's health and his projectiles are cannot be destroyed.

So here's a couple tips to defeat him more easily:

• Avoid spamming projectiles. Like I said above, his projectiles are invincible, so even if you use an EX projectile, his will always win;
  
  
• Apparently, spamming an uppercut move during a combo works best, specially to drag him onto a corner. I found the default Quantum Divine and Ancient Zen move set to work best, although, do replace Zen Mirror with Buddha Palm Combo, the Mirror will be useless for this fight;
  
  
• If The Last Human has full meter and randomly throws a stray projectile, chances are, he'll use his super afterwards, he will hardly, if ever, use it raw;
  
  
• He can use EX Special Moves for free, his meter is exclusively for the Super Move;
  
  
• Try to combo him after he does his punch barrage, and wait a second to see if he'll use the EX punch, he'll be vulnerable afterwards;
  
  
• Don't be in too much of a hurry to hit him, his moves do a LOT of damage, and he'll quickly rush to punish you for just swinging away. Wait for him to come to you, then punish him;
  
  
• Don't bother using your Super Move, it does massively reduced damage against the boss, so you're better off saving your meter for EX Special Moves.

Since the game automatically saves replays, I decided to record the screen and share the video on Youtube, as a demonstration of what I meant in the tips section. Hopefully it helps

https://youtu.be/GCL3OWw1PxQ?si=N4QxapCk43EvEzfL