The Host (2006) aka Gwoemul at IMDB
This is a Korean blockbuster movie that starts with a real event of dumping toxins into the Han River (by the US Military) and makes a monster flick out of it. (It could be seen as a sort of Korean Godzilla.) The digital special effects were done by a San Francisco company, The Orphanage, which may have contributed to my seeing a lot of people talk about this film.
About fifteen minutes in the monster makes itself known in a big way, with no shyness on the filmmaker's part in showing us the thing. This is not Alien with half-glimpses of a lurking unknown. You can see this orca-sized tadpole-looking thing run rampage through a popular river-side park.
Our protagonist, Gang-du, is a lethargic guy who only comes alive for his daughter (Hyun-seo) and when facing the monster. Mom is long gone, and the two of them live with her grandfather (Hee-bong) who runs a food concession stand near the river and employs Gang-du. Two other children of Hee-bong round out the family.
Gang-du's first interaction with the creature is to throw a beer can at it. When, a few minutes later, it starts attacking people he is one of the few that does more than just run. He gets his face splattered with it's blood after attacking it, and sees it carry off his daughter.
The authorities believe it is the source for a new disease (hence a "host") and quarantine Gang-du and his family. They resignedly put up with it in their grief over the loss of the girl. Until Hyun-seo calls and says she survived.
From here the movie follows some familiar formulas but still manages to be entertaining. The monster is gross and resilient, the family unites (in action, if not always together), and the girl is resourceful and caring. Call it five extra tails out of seven.
Final thought: the US Forces in Korea do not come off looking good