You can use continues to get the stage clear achievements. After playing the game for 1 hour (60 minutes) your continues go up to 5. After 3 hours (180 minutes), they got up to 8 and finally, after 5 hours (300 minutes) you'll get unlimited continues. With those, anyone can get this achievement.
There's no way to check how much you've got left and the game doesn't seem to count idling in the main menu or pause menu, just actual gameplay.
Beat the game using Ruby to unlock R.A.D. Beat the game using Tempest to unlock Sensei. Be mindful that if you use continues, don't change the character if you're going for a character unlock.