The approach to the lighthouse is the entire section after you have spoken with Zane for the last time, and used the floating ‘ignite’ word to turn the lighthouse lights on, which will then turn at a slow pace and one hit kill any Taken in their path. This segment is much briefer than the ‘Gunless Wonder’ achievement from the main game, and is made easier with the presence of the rotating lights. You will constantly come across floating ‘clear’ words which break the rocks on the path ahead of you, allowing more light exposure.
The Taken spawns are numerous and random here. Use flares when necessary (or flashbangs if you have any left from the earlier bridge segment), especially in dire situations. There are several checkpoints along the way, so if you die you will only be taken back to a slightly earlier position. The achievement will unlock when you reach the lighthouse and Alan begins talking.