Volgarr the Viking

As said in the abbreviated walkthrough, you will need to complete a world with one or more Warrior Spirits (every three chests after claiming the fire sword) to have access to the alternate path, which is called the Path of the Valkyrie. Once you complete the level it will show you how many warrior Spirits you have at the top right of the screen. Instead of taking the lower path, just climb up to the higher path and the wall will open for you.