This 50-minute animated The Little Mermaid film came out in 1992, and seems to have its own following of sorts. This film is usually referred to as the Golden Films version, though I've also seen it referred to as the Trimark or Dream Town version.
The mermaid of this story is Lena, youngest princess of the underwater kingdom. She visits the surface for the first time when the sea witch Cassandra sends her up in a magical whirlpool. Once there, Lena forgets about her birthday party she's supposed to attend, because she's enthralled by handsome human Prince Stephan, who's on a ship. When a storm hits, Lena saves Stephan and his manservant from drowning, and vows to find a way to see him again.
This is a pretty straightforward retelling of the Little Mermaid story, with the major changes being that Cassandra "forced" Lena to visit the surface instead of Lena going there by herself, Lena and Stephan's story is a straightforward romance, and the rival princess has a love interest of her own that makes the happy ending for everyone easier to achieve.