There are two ways to start the Dread Swamp Path - there's DSJ and non-DSJ.

I'll present the non-DSJ method first as it's substantially easier and the DSJ method only saves 15 seconds, so it should be reserved for attempts at WR, just in general.

Method 1: non-DSJ + Nuka

Method 2: DSJ

Tree Jump + Candle Movement

Hub

When entering the hub - as normal - Press Start and load the game to skip the cutscene.

Make your way over to Lair of the Beast.