This footage is from my recent MGS3 European Extreme difficulty Foxhound ranking run. This strategy may take quite a few tries to get down, but it's definitely worth it if you're struggling with this fight, and also if you're aiming to get that elusive Foxhound ranking.
The End always starts in the same sniping spot, regardless of difficulty; on top of the cliff in Sokrovenno North which can be seen if you turn around from your starting position. You can use Thermal Goggles to help locate The End, and to track his footprints as well. You can also cook a grenade and run with it to make your footsteps silent.
(Feel free to skip to 01:28 in the video if you know where to locate The End's first sniping spot.)
When the fight starts, immediately run towards the bunker on the left side, and start crawling before you emerge from behind the rock, otherwise The End will see you. Keep an eye out for the trap on the ground near the tree as well. If you need any ammo, you can crawl up to and into the bunker to get some, then crawl back out. Crawl until The End can no longer see you, then start running into Sokrovenno North. In Sokrovenno North, run forward and then to the left, up the hill and back into Sokrovenno South.
Sneak up on The End and use a Cig Gas Spray on him to damage his stamina, then hold him up with the MK22. Point the gun at his head and he will say "I don't think so!" Move your aim away and back onto his head, and he will say it again. The third time you aim at his head, he will yield and give you the Moss camo. Make sure to equip it, as it will provide a good camo index in these areas, and it also helps you regenerate stamina naturally.
Shoot The End 3 times in the head and he will tumble over. The combination of the Cig Gas Spray and 3 gunshots is more total stamina damage than just the normal 3 gunshots. He will then say something, throw a Stun Grenade, and then run away; follow him to his next sniping spot, and make sure not to look in the direction of the grenade to avoid being temporarily blinded.
The rest of the fight is pretty much RNG to be honest; The End tends to go to the same second sniping spot almost every time, but for every subsequent sniping spot, there's no real guarantee he goes to the same place every time. It may be somewhat difficult to track him, but the Thermal Goggles will help as mentioned above.
When you do find him, sneak up on him, use the Cig Gas Spray to damage his stamina, then hold him up again; he won't give you any more items though. Wait until he's fully on the ground, otherwise you'll only be allowed to get 1 shot off instead of 3.
If he happens to be in a spot where he's actually looking in the direction you're coming from, and there's no other easier or quicker way to get to him, like what happened to me in this video, you can throw a Stun Grenade at him, wait for it to go off, then quickly run up to him and Cig Gas Spray him or shoot him 3 times in the head.
Also, I'm not fully sure how he noticed me approaching during the final part; I had the Stun Grenade cooked and I was running with it, so my footsteps were silent. He must have noticed me out of the corner of his eye or something, which almost ruined the entire boss fight, but thankfully I managed to stun him before he stunned me, and then I managed to END The End.
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