Ok. First thing, we all know how hard it is fighting Liquid in the final battle on The Boss Extreme difficulty. You wouldn't believe how happy I felt when I finally managed to beat him, so I thought I should share some of that joy with you guys and hopefully you'll beat him.
Phase 1: Solid Snake
Your main attack is pressing R1 five times. Quicly dash with X over to him when he's down and right when he's done wiping sweat off his face, unleash your combo again. Repeat this until he just stares at you while you kick him. When this happens, dash away quickly to get away from his punches and repeat everything from the beginning. It's probably best that you don't grab him in CQC only because when Snake has him in a chokehold, you have to bring down his O2 gauge to begin bringing down his life gauge. On extreme, Snake has enough time to take some air out of him before he elbows you to the ribs, so this will bring down your health and none of his. I know, it's lame. When you get knocked down, if you press X quick enough, Liquid will do a taunt. Press triangle as soon as your up on your feet to regain some health, which is a HUGE help. But, the first time you get knocked down, you cannot get up with X. You wait for a while and press triangle. When your knocked down on your butt, Liquid will not attack you, so dont worry. I like to try and make sure my life gauge is almost full before going on to the next stage. When you get Liquid's life gauge down to half, he'll be a bit more aggressive, and you will need to dodge more. When this happens, you can heal yourself, or throw a few body punches by dashing and pressing R1, taking you to Phase 2.
Phase 2: Solid Snake
In this phase, keep a safe distance from Liquid. Don't even bother getting close to him in this whlle phase. He has a massively powerful punch, but you can learn to easily dodge this. He'll say,"Take this!" and lunge at you. When you hear him say that, dash left or right and he'll miss, giving you the perfect time to use your combo from Phase 1. If he hits you with this punch, you will lose a lot of health. Even if your life gauge is completely full, two punches will kill you, so be extra careful. Bring his health down really low and you'll go to Phase 3.
Phase 3: Naked Snake
Phase 3 is the phase I hate the most because he uses CQC. Keep a safe distance, like Phase 2, and use your combo repeatly, even if you're too far away. He might come towards you to grab you, but if you're lucky, one of your kicks will knock him down. Use the same method as Phase one and use your combo when he gets up, but be extra careful. If he grabs you, he'll kiss you on the cheek, and I think it brings down your life and psyche. If it does, you'll lose a lot of it. If your life gaug reaches zero, you'll still be alive as long as you have psyche, but in this fight, there's no calling Rose to get tips on keeping your psyche up.
Phase 4: Old Snake
You may think you're done with the hard part, but you have no idea what little surprise you have waiting for you. Both Liquid and Snake are worn out. As soon as you're in range, punch him. He'll probably punch you right back without even giving you the time to blink your eye. Make sure you're in range and punch again. It should go back and forth, you punch, he will punch, and soon the fight will be over. Congrats.