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Ended up beating Burgh with no casualties. I opened with Azumaril to take out his Dwebble and bait out the Levanny, but the Dweebble survived due having sturdy allowing it to use spikes and Burgh to use a hyper potion then switching out for Levanny.
The Leavanny was going to be the biggest problem but Luckily it went for Leaf Blade when I switched to the quad resistance fire/dragon Charmeleon, it out sped but I was able to OHKO without taking any more damage thanks to it using swords dance.
The worst case scenario was the Leavanny swords dancing on my Azumaril followed by it using aerial ace on my Charmeleon.
Had to switch in with my Zubat to deal with Burgh's masqurien and it barely survived and after that his Parasect died to my Vital Spirit Magby and his Larvesta died soon after. My Pidgey and Dwebble were emergency sacks I'm glad I didn't have to switch into. Even without the good RNG I got for my encounters, the fact that Charmander is available right before you fight Burgh, alongside an Eevee and an Evolution Stone of your choice makes him pretty manageable. Although I saved the Eevee to be an Umbreon later.