Level goddesses are quite op. I was using Willis to level up cards on boss fights (for unlimited turns) earlier, but she can increase rank only up to 30. Mikan has higher rank limit, she can raise up to 45, but her skill is auto with 25% chance, quite unpredictable and has nasty side effect of dealing 20% hp retribution damage to your team as gods find raising rank this way illegal. However there is a way to stay up with hp indefinitely. Obviously Kimchi with her 15% auto heal helps, but that alone is not enough to keep you alive. But both 2/2 Sill card and AL bishop (with 2AP initial) have a heal that is strong enough. Cost of heal goes up every use, but it stops at 9AP, so if you use medal for 6->10 AP you can use it as many times as you wish.
You might need to find a sweet spot in your initial team for the battle, as having too much hp compared to your healer power can break the balance, so you can start with some empty slots to lower hp and then add people mid fight as this will keep your total hp unchanged. At the same time you can't go with too few hp as the boss will still damage you. If you do it right and keep your interruption rate low so the boss doesn't die too early you can have every single card you have raised to rank 45.
There is also a boss before Pi that doesn't have any attack of his own, uses only summoned robot girls and other helpers which can be easily removed with Crane or any other unit with cancel enemy buff skill. He stops summoning after turn 20 and also has a weak heal once he has less than 50%hp so interruptions won't kill him. Looks like this fight was designed to take full advantage of Mikan skill.