“I need your help to catch a killer of women, Lisbeth.” The guts of ‘The Girl With the Dragon Tattoo’ are laid bare within the appeal for assistance by Mikael Blomkvist (Daniel Craig) to Lisbeth Salander (Rooney Mara). They each need the other, but not for the reasons that are initially presented.

Mikael is a magazine journalist in Sweden who suffered public disgrace after being convicted for libel against corrupt, powerful businessman Wennerstrom (Ulf Friberg). A large settlement was also awarded, and his magazine, already in severe financial distress, is in danger of folding. Henrik Vanger (Christopher Plummer), an arch-rival of Wennerstrom  and now retired, seeks out Mikael and offers him a sweet deal: Financial salvation and incriminating evidence against Wennerstrom in exchange for solving the case of his missing grand-niece, who disappeared in the 1960s.

The only catch is that Mikael must stay on the Vanger family’s private island, located in a rural part of Sweden. So he bids a temporary farewell to his business and domestic partner Erika Berger (Robin Wright) and heads off to an isolated cabin in the dead of winter. Multiple members of the Vanger family live in a compound on the island, but the one who stands out is Martin (Stellan Skarsgard), Henrik’s nephew, and now running the family business.

Mikael makes progress on his investigation, thinly disguised at Henrik’s request as ‘writing a memoir’ of the old man, coming to believe that Henrik’s grand-niece may have been the victim of a serial killer. But he begins running into dead ends and recognizes that he needs help to achieve a breakthrough. Thus the meeting with Lisbeth, who has done research work for the Vanger family in the recent past.

In her early 20s, Lisbeth is still a ward of the state, for reasons that will become apparent. She receives money from a trust fund, and when the guardianship of the trust is passed from a kindly older gentleman to a burly younger man named Bjurman (Yorick van Wageningen), troubles begin anew for Lisbeth, troubles that will reveal the depths of pain that she has suffered in the past and that she is willing to inflict upon others in order to protect herself in the future.

Lisbeth is a complex character; she draws from seething undercurrents of anger, anguish, and anxiety, while on the outside she appears to be withdrawn, flinching at the touch of a male stranger yet eager to spend the night with a female night clubber. She is brilliant at what she does, able to hack through computer security systems with the greatest of ease, analyze the information she finds, and summarize the results in concise form.

Rooney Mara is outstanding in the role, capturing the character’s abrupt, if subtle, changes in mood and temperament, all while suggesting the whirling tides of emotion that surge within and maintaining a rigid, physically fit (if scary thin) body posture. It’s one of the top performances of the year.

According to interviews, writer Steven Zaillan adapted the 2005 novel by Stieg Larsson without regard to the 2009 Swedish film version, directed by Niels Arden Oplev. I’ve seen the first movie but haven’t read the book, so I can’t comment specifically on the differences between them, though there are, evidently, significant differences. Beyond multiple key scenes and plot points, however, what the movies hold in common is a convoluted mystery that is less than compelling, filled with red herrings and complex family relationships. Perhaps on the page it’s easier to track the family tree and the relationship of one character to another, both in time and space. But on the screen, it’s easy to get lost.

But, considering that I’d already seen the Swedish film, watching the new version made the plot easier to follow; I knew which characters are most important to the story, and which ones could be safely ignored. David Fincher’s direction is marvelously fluid and Jeff Cronenweth’s digital photography — he took over after Fredrik Backar had completed 20 days of the 145-day shoot — is a wonder to behold, fully conveying the icy beauty of a Swedish winter. Editing by the team of Kirk Baxter and Angus Wall, who won Academy Awards for their work on ‘The Social Network,’ maximizes the dramatic tension and narrative flow of the picture. Add to that the unnerving musical score by Trent Reznor and Atticus Ross, which adds another level of unease to the proceedings.

Brutal and grueling, poetic and profane, ‘The Girl With the Dragon Tattoo’ is not the easiest film to watch with eyes wide open during the holiday season — or any other season, for that matter. Still, it’s one of David Fincher’s more haunting films, as likely to leave scars as it is to move hearts.

‘The Girl With the Dragon Tattoo’ opens wide tonight across the Metroplex.