A Steam Guide on using the developer mode states that it doesn't affect earning achievements, at the time of its writing (May 14th, 2018):
Achievements are currently not disabled with the console.
On the The Forest Wiki on Gamepedia, there is no mention of it. It only warns the user against adverse effects when using the commands wrongly, as some directly address achievements or their logging.
Furthermore, since there are commands that let the user immediately obtain certain achievements, one can only assume using the developer mode does not disable their attainability.
In your case, I'd suggest looking into the command
achievementloglevel all, which logs achievement progress and lists errors.