This is in stage 6. You must defeat the final bosses final form without being hit. He can deflect bombs and takes little damage from standard attacks so this will be tough.
Here is some modified advice from helgor;
Make a save right before this boss and practice this spot over and over. Learn the patterns and safe spots. As a precaution to make sure you have it down; don't make an attempt for the achievement until you can beat Amagisu' final form 3 times in row without getting hit. Not only will this save you time re-playing the entire game but also allows you to focus purely on learning his patterns.
You cannot use bombs at all during the fight.
Continues do not matter; leading up to the boss fight.
Using bombs before the boss fight does not matter.
You must destroy the bosses entire form without getting hit. This means the achievement starts after you kill Guwange-Sama (giant baby head monster), you must not get hit from that point on.