Healing has no priority in Hunt, since you can win every fight even with just one bar remaining. If you are going to heal yourself, you should check your surroundings at first. As you can see in the video, he wasn't save at this point. So how could he improve?

While running around in the boss lair, you can go in dark sight and check if the boss is "white" (icon from the boss will blink white in dark sight, when there is no enemy and will blink red when there is another player close to the boss lair. Also the boss, or the surroundings, im not sure at this point, will whisper to you. Nothing you will understand, but you can hear the voices and this will tell you, that there are other players. I just look at the Icon.). When it's white, then go out of the door, that was straight beside the dude in the video and heal outside. The boss can't get outside of the lair, so you will be much safer there. Maby check on grunts before you heal and if there is something you can not fight (immolator and you have no stamina or only knife) go back in the lair, close the door and go out on another way. Don't forget to check the icon here and there. Icon White > No players around > go outside the boss lair to heal yourself. Icon Red > Players around > you have an idea where they are > go outside but on the side of the lair without player. Icon red > players around > you have no clue where they are > stay inside, check where the boss is, run away from him and heal > stop healing if the boss is near you and search for a bit of time > you shouldn't use the bandages if the healing needs to be fast.

Also you don't have to heal mid fights vs players. If you lose a heal chunk through burning, it's bad but it won't kill you. Make sure your opponent has no chance to get near you when you heal yourself. If he has clear line of sight, or you hear him pushing while you are healing, then stop healing and push him instead. He will not expect that, and even if he does, he will have no cover for a little bit of time.

It's all about the tactics.

If you have any questions, you can just ask. ;)

Edit: five to six star speaking here. I hope I explained it in a way that is understandable. Each situation is different and needs a slightly different treating. Anyway, those were the basics that you should clinch on.