I just finished MGS2 for the first time last night. The worst fight for me was Vamp. I also had a lot of trouble with the Metal Gear Ray(s) fight until I figured out the trick.
Regarding Fatman - I found this fight incredibly easy. I'm not sure why people think it's so troublesome unless they missed the trick. The game suggests you need to first person aim to knock over Fatman - that's BS. All you have to do is plug him with the SOCOM 4 or 5 times using the auto-aim in top down view and he'll fall over, at which point you then easily shoot him in the head.
Harrier was also very easy, beat that one first try. There's no "trick" to that one, so I have no guess as to why people had trouble with that one unless it was rebalanced in the HD version or something.
Vamp fight was really rough. I ended up having to look up hints for that one. Turns out if you throw/shoot grenades in the water, they'll cause Vamp's O2 to run and he'll jump out of water and be slow for a short moment allowing you to get some easy shots in. Even then I still went through all of my rations.
Ray was also tough until I figure out that you shoot them in the legs, which causes them to "roar" at point you shoot them in the head and it does way more damage. You can take them out pretty quickly once you learn that.
Solidus was very easy, it's like an easy version of every Dark Souls fight. Just figure out which animation leaves him open to attack, walk around and hit him in the back.