To get it out of the way, you have to find a Sperm Whale in that area and blow the Sea Whistle. This part is quite tedious and is recommended you get air before doing it, just the fact that you have to be in the perfect spot so the whale comes. When you get it, the whale will come and fight with the Squid.
After that, you may focus on the two creatures fighting, and when you do, it will say, "Deep Sea Battle."
You can find these two fighting again, but it is unknown exactly when.
Though a popular scene in art, motion pictures and even some museum dioramas, this sort of battle is very sensationalized. In reality, Sperm Whales ambush the squid and kill it quickly. They are not "natural enemies" - the squid is the whale's natural prey. However, many Sperm Whales bear huge sucker scars on their skin made by Giant Squid, indicating that this scenario does happen at least sometimes, even if it is rare. Perhaps only exceptionally large individuals are capable of holding their own against the formidable whale or at least putting up a good fight before going down.