*WARNING - IT IS POSSIBLE TO COMPLETE THE GAME WITHOUT UNLOCKING THE INVERTED CASTLE*
If you do not do the following requirements, not a problem, reload your save and and redo the fight.
Yes, it is possible to beat Richter and not unlock the inverted castle, following these instructions will prevent you from doing so.
http://shrines.rpgclassics.com/psx/castlevsn/walkthrough.sht...This link will provide you with a simplified walkthrough along with a map containing directions on the path to take.
When you finally obtain the gold & silver rings, make your way to the clock room, equip the gold & silver rings, when the path is opened up after 13 chimes, drop down, and obtain the holy glasses from Maria (these are VERY important). No make your way up to the castle keep area, and to where you first fought Dracula in the prologue, you will have to fight Richter here now STOP! Equip your holy glasses, you will now see a green orb floating around (this is Shaft the dark priest) focus your attacks on shaft (not worrying about Richter) and the fight will end, you will now unlock the inverted castle.
Now the reason why it's missable is because, if you defeat Richter without equipping the holy glasses to see shaft, you will defeat Richter without defeating Shaft, completing the game without unlocking the inverted castle. So don't make that mistake.
Good luck, Shaft is a piece of cake.