This achievement is a grind. As the description states it requires completing all personal missions and getting all agents to level 20. The personal missions are available in the Missions portion of the pop up menu once you have unlocked the agent. The agents level can be checked in either the armory on the ARK or the Squad portion of the pop up menu.
Playing on a higher difficulty and having a high leveled ARK will net more EXP for your agents. Higher difficulty gives a bonus to EXP earned and agents that are underneath the ARK level earn catch-up EXP. When an agent reaches level 20, swap them out of the active squad and put another under-leveled agent in. By the time I completed the story line for the game and handled the personal and team missions, I was looking at roughly five agents left that need to be leveled up.
From some quick running around, the outposts, doomsday weapons and lairs seem to give the most EXP for the time I have been spending on them. Just rotating around what is available will help complete this achievement in the most efficient path possible.
NOTE: As others have been kind enough to test. This achievement only requires 12 agents total be leveled up all the way. You can replace any of the normal agents with the DLC agents to complete this achievement.
ALTERNATIVE SPOT FROM UnfurledEmu75: Best way to level up IMO, its playing two birds mission on max difficulty. When you go up to elevator use the rockets against the group of enemies on the first ice machine, that should net up to 1900 XP, after you reload the rockets use them with the group of enemies placed before the second ice machine, that gives up to 2600 XP, then reload checkpoint. So its around 4500 XP on less than a minute. And you don't need to bring any leveled character since the rockets do always the same damage, besides they're infinite.