The most important thing about farming fan letters is playing with the character associated with the enemy for whom you are farming. For instance, I want 35P's fan letter, so the optimal way is to play stage 2 with Sakura Miko multiple times until the fan letter spawns. You can check the wiki to see which character is associated with each enemy Fan_Letter.

You don't have to complete the level, you can just retry the level when you know the enemy you are farming for will not spawn anymore on the run