What the achievement asks
Raise five war campaign champions to Epic rank. Ten points, account-wide, both factions.
Champions are the followers you recruit through the war campaign, and they sit on the mission table in your faction's base. Rank goes up as they complete missions.
It comes after the war campaign, not during it
You cannot start this until you have champions to raise, and champions arrive as the war campaign progresses. In practice that means the campaign has to be well underway before this achievement is even visible as a goal.
Alliance players get there through Come Sail Away and the zone stories; Horde through Welcome to Zandalar and theirs.
Rank comes from missions, and missions take real time
Each champion climbs through the ranks by being sent on missions and coming back successful. Missions run on a clock measured in hours, so five champions to Epic is a matter of weeks of sending them out rather than an evening of play.
Send everyone on something every time you log in. An idle champion earns nothing, and the whole achievement is the sum of missions completed rather than any single accomplishment.
Rank is not cosmetic
A champion's rank affects the success chance they bring to a mission, so raising them is not only for the achievement: an Epic champion contributes noticeably more than a Rare one with the same ability.
That makes this one of the few Battle for Azeroth achievements that pays for itself while you do it. The missions get easier as the champions improve, which makes the last two ranks faster than the first.