This achievement is for getting to level 5. As stated in my Unstoppable Wanderer and Commonwealth Citizen guides, "The ways of doing this are winning charisma checks, killing things, turning in quests, lockpicking/hacking, crafting and discovering locations. In this Fallout installment, higher difficulties DO NOT give more experience. To my knowledge, it only decreases your health regen rate. You could go into the luck tree and grab the Idiot Savant achievement. It helps you get experience as long as you have low intelligence." As also stated in my other guides, here are 2 guides from IGN that will help early game. The first is for the Cryolater right after getting Dogmeat. (he is at the gas station right outside Sanctuary)
http://www.ign.com/wikis/fallout-4/Stealing_the_Ultimate_Wea... And the next is for the Power Armor within the first 5 mins