Similar to the boss fight in MGS with Psycho Mantis. You had to switch your controller to the second player port for that boss fight, so he couldn't "read your mind," and perfectly block all your inputs from the first player port.

There may have also been some save cartridge shenanigans, as it was a PS1 title

I think The End is obscure enough for people who haven't played it. Fun fact: this is one of the very few uses of the RTC setting on the PS2 affecting gameplay.

I exhausted all the ones I know in the PCSX2 2.4 blog post:

The PlayStation 2 uses a real-time clock (RTC) to keep track of the date and time in the real world. Games often use the RTC in order to seed pseudorandom number generation (RNG) because of its high variability. Additionally, save files show a timestamp in the BIOS, and these timestamps are sometimes shown in-game too. However, some games use the RTC in a more interactive way. Ratchet & Clank 2 and Ratchet & Clank 3, for example, let you teleport to the post-game Insomniac Museum area from 03:00–04:00, bypassing completion checks. The Simpsons: Hit & Run, The Simpsons: Road Rage, SpongeBob SquarePants: Battle for Bikini Bottom, and Scooby-Doo! Night of 100 Frights have holiday-exclusive Easter eggs. Need for Speed: Hot Pursuit 2 displays the date and time on a camera recording when you get busted. And Metal Gear Solid 3... if you know, you know.

Kingdom Hearts has a similar mechanic, but it uses your in-game time's hours mod 12 to give you a reward at the clock tower.