Overseer G50:
Level up a Dweller from Level 1 to 50
Your dwellers will gain experience from doing a number of things in and outside of your vault, such as, crafting items, producing food, water, electricity, and medical supplies, completing quest objectives, and killing threats inside and outside of the vault. They won’t, however, gain experience if they are in one of the Special stat training rooms. After a dweller has gained enough experience they will have a LVL UP icon appear above their heads, and when you highlight them it will automatically level them up. Dwellers obtained from a lunchbox that are higher than level 1 WILL NOT COUNT. Getting a dweller to level 50 will take a while, but once one hits level 50, your achievement will unlock.
Quests and Wasteland exploration are the quickest way to level up dwellers, while vault door guards, living quarters dwellers, store room dwellers, radio room dwellers, and dwellers in training rooms receive next to no experience (if any at all).