It felt weird that the True Final Boss is just called "The Lich". No Punny Name, he's just "The Lich". Then it hit me that he follows the same naming conventions as the playable characters, which makes sense, since he's implied to be the very first Gungeoneer.
All of the Gungeoneers have learned a Chekhov's Skill from their time in the Gungeon during their past — The Convict uses the table flip to surprise her enemy, The Hunter uses a Blank to escape a trap, and The Pilot uses the dodge roll to avoid certain attacks. The skill that the Marine learned is, well, general combat ability. Judging how his team let him stay behind to go fight the Horror without him, he was probably considered the weakest or least experienced of them all, and his team wanted to keep him alive.
Of all the characters, The Convict is the only one who doesn't get the option to repeat the mistakes of her past. Why? Because she has a constant reminder of it, in the form of the photo of Black Stache captioned "Don't believe his lies" that keeps her rage alive and in the front of her mind.
The Bullet also learned as well. While the Blasphemy shoots sword beams and can cut bullets in the present day, it lacks the ability to do either in the Bullet's Past, and given how the Blasphemy is the only weapon the Bullet starts with, he likely learned how to live without those little perks during his trek through the Gungeon. Also, when Cannon is killed, the Bullet impales him in the head with the unpowered Blasphemy, which promptly powers it up — the Bullet sealed a Stable Time Loop by killing his own Past! It could also be that The Bullet doesn't have a regret in his Past since there's no signs of Cannon in the present and he still has the powered up Blasphemy, so going to his Past is just reliving his already successful glory days for some fun.
The Gunslinger is the inversion of this. After being yanked to the present by the paradox, he sees what he's destined to become as the Lich. Be it that he witnessed himself become a monster, or that he witnessed himself getting killed over and over again by the gungeoneers, he decided he'd rather not and simply throws down his gun and departs.
The High Priest doesn't seem to follow the Punny Name setup of his fellow bosses either. The name seems like a trick to cover up his gun for a head. But working with that and his magic ability, an alternate name could be: The Warglock.
The Dart Gun seems like a very poor choice of firearm to start with, but including the entry below in Fridge Horror, it’s implied through the descriptions of the 3rd Party Controller and Light Gun that the Dart Gun was instead a fallback weapon after the Cultist accidentally dropped them into pits.
The Cultist's starting equipment includes a dart/nerf gun and a cookie. They are surrounded by toys, crayons, and a juice box. They can only enter the Gungeon if accompanied by another character. The Cultist is a child!
The Pilot's ending might not be such a happy one...yeah, he saved his partner, but he just destroyed a Hegemony battleship, likely making him one of the most wanted people in the galaxy.
The "Escape Rope" item looks like a noose... The fact that it shows up in shops only makes the suicide implications worse.
The reticle that appears when a character is killed is the same as the one that appears when a character picks up the Gun That Can Kill the Past. This, of course, justifies the same Gungeoneers taking multiple runs trying to kill their pasts, as it's implied that it is The Gun that is resetting them, but in that case... who is shooting them?
You, the player, are. You're helping them achieve their goal by undoing their mistakes.
Alternatively, there's a hypothetical timeline where they got the Gun That Can Kill the Past, then looked back and realized they failed and died on the way, and use it to prevent that; and this repeated until they had a successful timeline where they didn't need to eliminate a mistake in the Gungeon and could focus on their original goal.
Anyone else, if someone went back and killed their past it would change history slightly, your characters being saved by the butterfly effect of another gungeoneers victory.
In all likelihood, it's potentially The Lich. He's got the most access to The Gun being the Gungeon's Master, and it's likely in failed runs he has enough time to fetch it and cast its accompanying Bullet.
