They will die but it takes ages. I suggest changes in weapons or even just quit the map. That’s what I do 
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kkkkkkkkkk, obrigado!
if the map has Heal affix, that can make the Epic, Legend, and Mythic monsters harder to kill. maximum is 5% heal for all monsters on the map. at floor 3,000+, Legend and Mythic monsters have so much HP that the 5% heal means they are healing more HP than you can damage when their HP gets around 1% to 10%. at even higher floors, even 1% Heal can be a problem. it is like when a monster has Thorns and causes you damage, but you have enough heal that when your HP gets low, you are healing faster than Thorns is damaging you.
basically, Monsters have the Leach Affix, which is like the players HP on Hit affix. but at high floors, monsters start one hitting you. you can see if a monster has this affix when you are fighting them. the Heal affix from the Map is Regeneration of 1% to 5% of their max HP, and you only see it listed on the map, not on the monster when you are fighting it. I recently had to give up on a map with Heal while fighting a Mythic monster around floor 985 M3, so I feel your pain.
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@Golem explains things so well. But yes, sometimes you have to know when to give up on a map. I gave up on floors 1300
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NA VERDADE DESISTI DE VARIOS ATÉ AGORA 
in that case, it could be a bug. just put in a bug report in the report bug thread.
I’m up to map 1508 and the heal maps do seem buggy. Sometimes I just open my inventory and the monster dies for no reason. Sometimes I go kill other things then come back and kill it easily. Sometimes I just try different equipment combinations. Sometimes I stop attacking for a few seconds then attack it and it dies. Sometimes I just give up. What seems to work best is to pull them apart and fight them one-by-one but sometimes that doesn’t work either.
I check my Codex progress to see what will be spawning on the map before I open it. If there’s a legendary Enslaver or a mythic shrine monster about to spawn and I have a map with heal on it, I’ll buy another map rather than risk not being able to kill them.
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Heal isn’t a problem for me on lower floors, but it is on my list of affixes to avoid at higher floors. I didn’t think I would get a Mythic monster when I decided to let Heal stay on the map. poor, poor me. 
You can spend 30 minutes on a high map and drop crap. Is it worth it ?
well, I spent about 40 minutes, until I woke up and realized that the Mythic was still alive, trying to kill it. when it starts to take too long to clear a map, then I know it is time to make a more powerful build. I have been focusing on Farm Builds for now just for getting loot, and I want them to be able to do well on floor 1,000. doing well on floor 1k means monsters on floors 500-510 don’t stand a chance when I am farming for Ultra Rare Crystals and Myth Stones. stubbornness is both a blessing and a curse.
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I know, crazy right? But if the challenge stops then I get bored. This endless game is great for me.
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Theres is a tips and trick how to kill legend, even mythic enemies under 3sec…
Soon i will post thread about easy way hiking+farming on high floor.
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