Quick idea that might serve both sides...
Boss phase determines behavior
E.G. eye of cthulhu runs away at dawn in phase 1, but swallows you whole at dawn in phase 2.
Bosses are an absolute nightmare for players who aren't prepared for their auto-spawns, so only players who are capable of getting the boss low should have to risk the instakill.
This would save many hardcore runs from a mistimed skeletron prime
All of these activate if the boss has not been killed in 8-12 minutes
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Eye of Cthulhu
1. Runs away
2. Swallows you whole after following at about half dungeon guardian speed, but health and defense remain the same, so you can still win
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EoW
1.(More than half of body segments alive)
Flees underground
2.(less than half of body segments alive)
Spawns 2 devourers and one eater for every segment killed so far, and remaining segments separate and act like one segment worms
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BoC
1. Runs away
2. Gains the moon lord's tongue effect, but it just gives health from healing items to the boss instead and prevents escape and magic mirror use
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Skeletron
1. (Hands intact)
Flies down into the dungeon
2. (Hands destroyed)
Headbutts at the player like the EoC's charge, losing all defence and dealing half damage without any headbutt cooldown
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WoF
It already has its own system
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The Destroyer
1. (More than half probes alive)
Flees underground
2. (More than half probes killed)
Launches a probe from each segment, and each segment releases a new probe when the old one dies
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The Twins
This one's hard, so I'll list a few possibilities
(Retinazer gains an ability like the moon lord's eye or the martian saucer, just reddish purple and thinner, and spazmatizm's fire sticks to blocks)
Both eyes phase one
Flee
One eye phase two
Other eye enters phase two regardless of health
Both eyes phase two
Eye at lower health dies and its remaining health goes to the other eye, which now starts to act like I mentioned above (spazmatizm starts painting fire on things as well as targeting the player, and retinazer sweeps the mega beam back and forth every few seconds)
One eye alive in phase one
Health refills and same as previous
One eye alive in phase two
Health does not refill, but spazmatism's fire attacks all happen constantly and simultaneously for the rest of the fight, and retinazer now exclusively uses the mega beam accurately with short breaks between firings
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Skeletron Prime
Same as normal Skeletron
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Plantera
As plantera has no flee mechanic, I'll just skip her, but she gets the WoF's tongue ability in phase 2 to keep the player in the underground jungle
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Golem
Same situation, but gains the ability to use a tractor beam on the player in phase 2 to keep the player in the room
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Cultist
The flaming tablet leaves a portal behind after breaking that fades through the pillars' color spectrum throughout the fight
If the cultist is below half health after ten minutes, the portal will spawn an enemy based on the color
Solar: Crawltipede with no weak point
Stardust: Star Cell, but the last two baby cells remaining are super glowy and can't be killed unless the boss dies
Nebula: spawns a Brain Suckler that can be knocked off your head for about twenty seconds but not killed
Vortex: same as Stardust, but with two Alien Larvae
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Moon Lord
Will occasionally swing hands like Skeletron, but if the hand hits you, the mouth hole in the palm swallows you
Open to replies and criticism, maybe apply this stuff only to expert mode or something