Fanfic Could have been decent, but the character bashing turned it to crap.
It's understandable that this author doesn't like Asuka. I have a bunch of characters I don't like, too. I dislike characters in a lot of ways - ranging from disappointment at how a character is managed, to sheer unadulterated vitriol at certain characters being poorly-disguised self-insert wish-fulfillment fantasy author avatars. If you don't like a character, do try to write a way for said character to lose the things that make them unattractive to you - doing so exercises your skill at writing character development.
But no, you just had to put Asuka through a pointless wringer and give her a pathetic end, all because you don't like her. True, I tend to save my most incendiary writing for said creator fantasy characters, but Asuka as a character isn't a lost cause. Some character development would have given her a better fate than what you've written.
All in all, you just took a massive dump on what would have been a decent crossover thanks to blatant and borderline misogynist character bashing.
P.S. I don't even like Asuka and her bad end in this story makes my fingernails curl.
Fanfic Horrible
This is a fairly cool concept, but it quickly went to hell.
The first mistake was flanderizing Asuka into an irredeemable bitch who was bashed by all of the "good guys", regularly got the shit beat out of her by Shinji, with only token nods to her own issues and ending with a fate that is so mean spirited and needlessly cruel that I can just tell the author had a bone to pick with her. Both Shinji and Asuska have tons of mental baggage. People treat Asuka like shit for her problems, before turning around to coddle Shinji.
The second mistake was that the "good guys" were far too powerful. I never felt scared for them or particularly invested. Big Boss gets himself a position of power that makes him outrank the man SELEE is using to front their plans for world domination, even though he himself should be a well established war criminal...because he's awesome. He can get a bunch of Metal Gears with anti-AT field weaponry that can kill the most powerful things ever known to man...because he's awesome.
The third was Shinji. I can understand if someone thinks Shinji is too whiny and passive, but this goes WAY too far in the other direction. Treating everyone around him, except the sanctioned Metal Gear "Good guys", like crap makes him come off like a twat. And his "badass" actions, come off as hilarious considering he's a 14 year old kid who was emotionally unstable a month ago, making him feel like a little kid trying to act tough. Also, he stares down Gendo Ikari and forces him to meet his demands? No. That does not happen. EVER! (Speaking of which, who the Hell takes a depressed kid who nearly shot up his class and teaches him martial arts!?)
The Fourth was the relationships. They were all pretty bad. Snake and Meryl just kinda get slapped together at the end without any build up (With Meryl's actual love interest getting murdered to make way for Snake. What the Hell?) Rei and Shinji also comes out of nowhere with no build up, despite Rei acting like she hated Shinji for half the story (In a completely OOC moment).
Wish I could fit in more, but I ran out of space. Bottom line, falls into way too many fanfiction pitfalls about bloated heroes, one dimensional villains, melodrama, no real tension, character worship, character bashing, and forced romance. I can't recommend.