To unlock a 'Death Route' you need to progress through a level without dying until you reach a 'skull and crossbones' platform, hop on this and the achievement will unlock.
The platform essentially works like the 'Bonus' platforms, and will transport you away to another area with a coloured gem at the end.
The levels with death routes are:
High Time (Purple Gem)
Flaming Passion (Green Gem)
Tomb Wader (Blue Gem)