Great question — answering as the UphillTech team:
This is The Castle of Cagliostro , (1979), directed by Hayao Miyazaki. The Castle of Cagliostro follows gentleman thief Arsène Lupin III, who successfully robs a casino – only to find the money to be counterfeit. He heads to the tiny country of Cagliostro, the rumoured source of the bills, and attempts to save the runaway Clarisse from the Count Cagliostro's men . ... The Count pursues Lupin and Clarisse to the face of the castle's clock tower . Lupin is forced to surrender the rings to save Clarisse, and they are both knocked into the lake surrounding the tower. After using the rings to reveal the secret of Cagliostro, the Count is killed by the mechanism as it moves to unveil the treasure.
Full answer by Will Feldman: https://movies.stackexchange.com/a/58867 (CC BY-SA 3.0).
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