S-TEC Pegasus for a megamorph equip/perhaps also get MBD from Low Meadow Mage/good luck.
My first time beating the game I relied on my Skull Knights (also from LMM) and a lot of equip cards. Quite a few are capable of enhancing his power, which is neat to me. However, MBD+megamorph does take less room up in your deck...
But my way did (does) work, you just have to be patient. As with all card games, luck is always there.
Skull Knight is the 2nd best monster you can use to defeat BEUD out of all of the confirmed cards. you just need 2 equips on it, same with MBD. zoa is 3rd best out of the confirmed cards at beating BEUD and many of the equips that work on SK work on Zoa
let him have at least 1 monster out when you end your turn. it triggers a different move from the AI, sometimes a fusion, monster equip, or pure magic. if you just blow away their monster all the time and leave them without a monster on the field, they wont fuse.
I have recently been STECing Pegasus and I have noticed he is a big stupidhead at fusing--some games he comes out swinging with Crimson Sunbirds and THTDs; other times he starts off ultra stingy and fuses to cards already in field or just plain does not fuse at all. Then there's the times he brings out MBD...et cetera.
It's difficult. Especially since he has 3 Raigekis, 3 Dragon Capture Jars...and I forget what else but anyway you get the point--his magic cards are annoying. I have 3 MBDs, Skull Knights, Zoas and I have equips for them all...including 3 Raigekis (just because, when I get upset, destroying his monsters feels so good) and still it is difficult.
However, every battle I've faced him he has fused. I am not sure how to manipulate the AI, but it seems standard to me that if you play face down cards, and do not attack him, he will fuse.
Problem 1: instead of fusing Pegasus will spam magic cards and/or set traps (invisible wire and fake trap are his best, laughably). This wastes your time and, more importantly, your life points. How to counter?-----hope. What I do is on my next turn i destroy his monster card (which attacked me after his raigeki/dragon capture jar made short work of whatever face down card(s) I had out) with something fierce, and wait for his next turn. Typically he will then play something face down in defense mode (as usual). On my next turn i do not attack and HOPE that on HIS next turn he will fuse. This...well I gotta be honest, it doesn't work every time (and can lead to problematic spamming of raigekis...or ::sigh:: other bad cards)...BUT it has the potential to. It's a constant battle between letting Pegasus destroy my cards,losing life points, and hoping he will fuse. THE INSTANT HE FUSES I ATTACK. Then, with a one card (or two card) lead I only need to worry about not dying (which isn't easy sometimes).
Problem 2: he simply does not fuse. How to counter?-----same tactic as problem one--destroy his card, wait a turn, hope for the best. Now, these tactics seem strange perhaps, but it has been working for me. Then again there is an FAQ about this, right? I would guess there are better strategies there.