A method posted by Xeinok 4 years ago still works today:
In your Steam library, right-click Garry's Mod and go to Properties > Set Launch Options and put in the following commands:
-noborder -windowed -novid -nosound -nojoy -noipx -nopreload -nod3d9ex -low -textmode -insecure +sv_lan 1 +map gm_flatgrass +achievement_debug 1
This will run the game while using the least amount of resources possible, the "achievement_debug 1" command will tell you your progress toward the achievement in the console.