Well without knowing the story itself and the character it's going to be hard to help with specifics. It will really come down to story and character, because movies, games and comics can get away with epic fights that are just there for the sake of it, but with writing you don't have the pretty visuals to distract the readers from fights that lack depth, so depth is quite important in writing.
If it's an epic climax, then hopefully the hero and villain should have already been established and you know what they want. I hate stories where the badguy's story is told during the battle (which means the badguy actually stops his plans to explain everything and the good guy is nice enougth to sit and listen) or after the battle (which means you spent the "epic battle" not even knowing who the badguy was, that only works if your trying to make the reader feel guilty for wanting him to lose.)
If both the hero and badguy is established well before the battle, then the reader is already pumped for the final battle just to see how these two guys go up against each other and the fight itself can do it's thing without distractions.
The actual battle itself again will depend on the characters, their fighting styles, their skills, strength and intelligance. You need that connection between the character in battle and when he isn't fighting. Final Fantasy VII: Advent children made the grave mistake of having Cloud Strife mope about for the times he wasn't fighting, it just made you wonder how a man who sulks all the time saying he is no good to be around people suddenly gets the engergy to fight like a god like perfect grace (even before given the prep talk by his friends) never the mind the fact he has been nothing buy a deilvery man for the last two years and it never once established he has been training. Cloud strife the person didn't seem like the same guy as Cloud Strife the fighter. His willpower just seem to come out of nowhere. So everything about your character needs to tranlate somehow into the fight itself, the way he talks, the way he normaly moves, the stuff that he's into and way of thinking, don't just have willpower and ablities that come from nowhere. If your characters are good, then they will help you make the fight.
Good fights are when the good guy and bad guy are equaly matched, don't make it too easy for the hero. The fight should tell some story of how the good guy defeats the villian (or how the good guy loses if it's that kind of fight.) So when writing the fight, always think about who's currently winning or losing and what they can do to fight back and gain control, that will give tention. The audiance will worry then the hero is currently losing and will cheer when he is starting to win. Don't write it like like some animes where the hero and villain are shrugging off hits for most of the fight, if noone is getting hurt then you don't know who is currently winning, it's just random meaningless blows until the badguy randomly loses, you don't know why he lost, it just seems like the author got tired of the fight and just finished it. So constant flow of battle, with both sides taking hits and having near loses and winnings will keep the battle interesiting.
As Jedi pointed out, the enviornment is very imporant. Characters with situational awareness is perhaps more imporant than any skill or weapon, even wrestlers will use the boxing ring to their advantage, using the ropes to give thrust or to climb and jump from the corners. The characters need to keep moving about, looking for anything that can give them an advantage, because if they just go up to each other and start trading blows in the hopes that they can hit each other harder than they can be hitten back...well this might happen...
https://www.youtube.com/watch?feature=player_detailpage&v=t6dabPhec7Q#t=5s
If the character is really trying to save the say, then there is no reason why he should make it easy for the badguy to hit him back. It's a fight for the fate of the world, not a sporting match where it doesn't matter if you lose. If the hero isn't taking the fight seriously, then why should the readers? Also the movement of the fight will keep it interesting and bring more variety than just having them standing there trading blows.
Also subtext can make a fight memorable, so your character is fighting to save the day, but what else is there? If it's the final epic battle then everything that's been leading up to it will provide the context. The first matrix film was about Neo becoming aware of his potential, so the final battle was when he finally unleashed that potential, that was the subtext. It can sometimes be as simple as that, it doesn't need to be really insightful or deep, but it's gives more to the fight than the hero just saving the day.
Anyway I hope that is of some help