Sounds like the original Swedish film was better.
I actually haven't yet seen the English-language remake of the 2009 Swedish film http://www.imdb.com/title/tt1132620/combined that has been shown on cable TV with the same title. The original Swedish title of the book was "Män som hatar kvinnor" – literally, "Men who hate women" (according to Wikipedia). But I read the full plot description of the American film on this site, and notice several changes that would leave out some of the more intriguing aspects of the mystery. Of course, I am basing my comments on the English subtitles that were added to the Swedish film, so perhaps some of the differences I'm noting are due to inadequate subtitles (but I don't think so.)
Mikael Blomkvist is a disgraced journalist who is asked by a wealthy industrialist to use the months before he is scheduled to begin a prison sentence to find out what happened to his niece, under a personal contract, not as an employee or contractor of his family's huge industrial group (Vanger) he heads.
In the Swedish film version, unlike the original book, Lisbeth (splendidly played by Noomi Rapace) is not hired by Blomkvist based on a recommendation of Vanger's. She hacks into his computer and sends Blomkvist information that eventually leads to the realization about serial killings. Lisbeth's own life is a separate mystery involving a depraved guardian, murder and rape.
Lisbeth is the one with the tattoos. She turns out to be someone not to mess with.
The Swedish film seems to have been made in parts. The version I saw ran both parts as a single film with just a title break separating them.