“Lucy” is now playing at Point, Eastgate, Star Cinema and Sundance. R, 1:30, two stars out of four.

Scarlett Johansson’s year at the movies has been inhuman. First, she played a sentient computer program in “Her,” then a predatory alien seductress in “Under the Skin.” Now, in Luc Besson’s “Lucy,” she’s a woman who becomes superhuman when an experimental drug unlocks 100 percent of her brain power. The days of playing zookeepers in “We Bought a Zoo” seem long behind her.

“Lucy” seems the most farfetched of the bunch, and not just because Lucy can instantly access the entire base of human knowledge or throw bad guys around the room with her mind. The film is an ungainly mix of Besson’s typical girl-with-a-gun action thriller and some trippy, dippy sci-fi, at times literally cross-cutting back and forth between the two. Think “La Femme Nikita” suddenly tripping and falling into “The Fifth Element” — it’s a candy-coated mess.

Things start off well, when we meet the pre-brainjacked Lucy, a party-girl college student living in Taiwan for whom life seems to have been an endless string of bad choices, starting with that leopard-print jacket. Lucy gets cajoled by her shady boyfriend into delivering a suitcase to a nasty South Korean gangster (Min-sik Choi, the original “Oldboy”). The boyfriend gets killed, Lucy gets captured and forced to become a drug mule, with a package of bright blue crystals in her abdomen. (Somewhere, Walter White is filing a patent infringement claim.)

This first 20 minutes or so is the best part of the movie, as Johansson convincingly plays a terrified, confused woman in way over her head, surrounded by some very dangerous men. (Besson exaggerates her plight by including footage of a mouse tempted by a mousetrap and cheetahs bringing down a gazelle. It’s “John Woo’s Wild Kingdom.”)

But then Lucy gets roughed up by some different gangsters, the drug gets released into her system, and her brain starts powering up beyond the 10 percent capacity that the movie says humans only use. (Not true, by the way.) We know this because, in the clumsiest manner possible, Besson cuts in scenes of a lecture by a Professor Norman (Morgan Freeman) on the potential for the human brain. At 20 percent capacity, he states, man can change his own cellular structure. At 30 percent, he can control the bodies of others. (I found his theories of the LEGOverse more believable.)

It would have been fun to see the formerly timid Lucy slowly flexing her new brain muscles, but she snaps into superwoman mode in an instant, able to shoot six men in six seconds, change her hair color, even appear on television screens halfway around the world. Basically, whatever power Besson thinks it would be cool for her to have (and might help paper over a plot hole), he gives it to her.

Lucy goes to Paris to find Professor Norman, Korean gangsters on her trail. The stronger and smarter Lucy gets, the less interesting she and the movie become. She’s basically invulnerable, so there’s no thrills in the action scenes (including a random car chase that looked heavily CGI’d up). And she grows colder, less human and relatable. I started to miss that scared woman in the leopard-print coat.

And also, for a movie that spends so much time noodling about enlightenment and human potential, Besson really has a retrograde fascination with killing. Hardly a scene goes by where an innocent bystander isn’t casually blown away, the low point being when Lucy shoots a cab driver because he doesn’t understand English. (The faint “My leg!” seems to have been added in post to soften her up a little.)

Besson wants to blow our minds, especially with a WTF finale that traipses across time and space, but he’s tethered to action-movie tropes that went out of style in the ’90s, frankly. It’s like he wants to make his own “2001,” but can’t resist putting in a climactic gunfight between HAL and Dave.