After successfully special summoning your Gate Guardian just simply let it on faced up attack position and continue stalling turns, wait for your draw engine cards like a normal monster White Elephant's Gift combo, Shard of Greed or Jar of Greed, to get your final turn combo pieces. This way you can easily achieve 8000k+ duel assessment.
Always set a Rai-Mei to either search for unhappy girl or to thin out your deck, or heal with enchanted javelin when they attack her. Summon unhappy girl once you have twister in your hand or if weevil does not have any set trap. Keep passing the turns to stall until you can summon BEUD while leaving 1 monster slot open on the field for vassal on the last turn.
If you don't have union attack, you can use Cu Chulainn with Blue-Eyes White Dragon, ritual weapon and riryoku instead. Twister can also be replaced with Wild Tornado.
Summon high attack monsters but don't attack weevil's monsters unless they're in defense position to not lower his LP. You can keep using otohime to switch his monsters to defense. Keep destroying his monsters so that on the last turn you can finish the duel with BEUD that's equipped with sword of deep-seated for 10,000 damage. You can lower your LP either by getting attacked or prolonging mirror wall's activation.
Summon high attack monsters and keep destroying weevil's monsters without lowering his LP, while lowering your LP to half or more of his LP. Finish the duel with a buffed Cu Chulainn using BEWD and ritual weapon.