If a 4 Might unit moves from base to Trifarian Warcamp, do they become Mighty and trigger Fiora's Legend ability?

Yes, moving a 4 Might unit from your base to Trifarian War Camp will cause it to "become Mighty" and trigger Fiora's Legend ability.

This is distinct from playing a unit directly onto the battlefield. When you move a unit that is already on the battlefield (your base) to Trifarian War Camp, it is already a game object in play. As it enters the War Camp, it gains the +1 Might bonus, causing its Might to increase from 4 to 5. Because the unit was already on the battlefield when this increase occurred, it satisfies the condition of "becoming Mighty," which triggers Fiora's Legend ability.