Some spoilers below on how to unlock Boss Rush:
To earn an A rank you have to complete the Boss Rush with a time between 6 to 7 minutes. As the name implies: You must defeat all bosses from the game sequentially and with essentially no breaks in between (minus a ~5-10 second animation for bosses to die and spawn in).
Same tips as the S rank guide by holywood apply (along with some others that I felt were useful):
1.)If you're having trouble completing it, it might help you out by grinding over at the extra stage area so you can have a higher DPS going in (Note it takes ~3 levels to increase your attack by 1 point).
2.)Spam Thousand Daggers!! when in normal time: you get some wicked i-frames and basically don't have to worry about damage until you exit the move (or run out of MP). Note that for many of the bosses you may need to jump so that the auto-aim actually targets them. Be wary of attacks/projectiles that can be destroyed since TD might decide to target those instead.
3.)It might benefit you to buy some consumables for Time, Health or MP if you're struggling with resources. (In my S rank run: I used 5 MP consumables and 1 Time consumable.) I found that a good place to grind currency was the area right before the final boss fight in the extra stage.
4.)Max out all of your bars by finding or buying the upgrades before attempting this, the extra 50 MP/HP is invaluable to finishing with a good time (and in my case: finishing at all lol)
5.)Whenever you stop time you can throw only one thousand dagger spam, but you can unpause and then repause time instantly to stack them.
6.)If you need some breathing room, don't forget that you can slow time by holding down and releasing the attack button
7.)If you need to cycle through your items to use a consumable: stop time first so you don't get overwhelmed with everything going on and get hurt (or even worse: die!)