Saving your game progress after beating a boss is like taking a selfie immediately after ordering a sandwich, or coming out of the train, or washing your face! (illgaming.net)
For example, now beating the bosses in the boss ring gets you an in game «achievement», as does getting a perfect S ranking on each of them. (gamingreinvented.com)
Honestly, I didn't have any problems doing this and even beat the bosses without any effort. (videochums.com)