This achievement is obtained through natural progression
You can level up your dwellers in multitude of ways; working in the assorted resource rooms, rushing said rooms, detering the various hazards (radroaches, molerats, rad scorpions, fires, raiders, deathclaws), sending them to the wasteland, completing quests etc.
This does not require you to level up any of the specific S.P.E.C.I.A.L stats through training rooms, just the overall level of your vault dwellersIf you need more explanation: