@akkartik I haven't seen The Rig yet, didn't realize it had sea monsters in it, will have to watch!
You're right, there aren't a ton of options to choose from. Underwater (2020) was decent. From back in the day, Anaconda (1997) and Deep Rising (1998).
Honestly some of the films are faint memories from childhood that if I rewatched I'd probably find much too corny. I liked Gorgo (1961), 20,000 Leagues Under the Sea (various), trying to think of others...I'll take suggestions :)