The most remarkable thing about her was that she was so strong. She was so very strong that in the whole wide world there was not a police officer as strong as she. Why, she could lift a whole horse if she wanted to! (1.9)
So that's pretty strong, especially considering that a horse would be really awkward to lift. (You know how sometimes it's more about the shape of an object than the weight? Like you could lift it if you could just figure out how to get a good grip on it?) But more importantly here, Pippi gets compared right away to police officers, and what do police officers do? They make sure people follow laws, i.e., they are crusaders for justice. And she's stronger than they are. (We'll let you take it from here.)
"I don't think you have a very nice way with ladies," said Pippi. And she lifted him in her strong arms—high in the air—and carried him to a birch tree and hung him over a branch. Then she took the next boy and hung him over another branch. (2.59)
So now Bengt is bent. Over a tree limb. Get it? In this situation Pippi uses her strength to take on five bullies at once. Well actually one bully and his minions, but there are five of them and just one of her. And she's younger. And smaller. And… way stronger. And we love it because this is the dream of any kid that's ever been outnumbered or intimidated like this: to meet the bully head-on and win. Calmly. And with a joke or two.
She climbed up the shingles almost as if she were a little monkey herself. In a moment she was up on the ridgepole and from there jumped easily to the chimney. (3.27)
Pippi's not just incredibly strong though—she's got mad climbing skills, too. This ability is a little easier to understand, seeing as how she spent nine years on a ship climbing the mast to check the weather, but it's still exceptional. And way beyond what one would expect of most nine-year-olds.
"Oh no, I'm sorry. I haven't time to play any longer," said Pippi. "But it was fun."
Then she took hold of the policemen by their belts and carried them down the garden path, out through the gate, and onto the street. There she set them down. (3.38-39)
In the first chapter we're told that there's not a policeman in the world stronger than Pippi, and here we get to see that statement put to the test. She doesn't just outwit these two officers, she outmuscles them, and remember—they're symbols of law and order. So that either makes Pippi a symbol of anarchy and chaos, or suggests that she might be advocating for a different sort of law and order.
"As I was saying," went on Pippi, "forgive me for breaking up, and also forgive me for breaking off," and with that she broke off one of the bull's horns. (6.52
Truthfully, we're a little creeped out by the idea of snapping the horns off a bull. Of course, Lindgren makes sure we know it doesn't hurt the bull at all ("as bulls have no feeling in their horns" (6.53)), but still it seems a little… aggressive. But Pippi's done two important things here: she's calmly rescued her friend from a dangerous situation, and she's taken an imminent threat and made it docile. Really docile. At the end of the scene the bull is sleeping like a baby.
The bull whirled round and round trying to throw Pippi.
"See me dancing with my little friend!" cried Pippi and kept her seat. (6.55-56)
Have you ever seen someone trying to ride a bull? Eight seconds is the length of time bullriders try to stay on. Eight seconds. Pippi stays on till the bull lies down and takes a nap. If she ever runs out of gold coins, she should enter a few rodeos.
But now two huge guards came to throw her out. They took hold of her and tried to lift her up.
They couldn't do it. Pippi sat absolutely still, and it was impossible to budge her although they tried as hard as they could. (7.37)
Pippi's physical strength allows her to go dead weight on these guys and hold her position. It's actually a great metaphor for the way Pippi refuses to budge on anything she thinks is important, whether it's attending school, living in a children's home, or going to bed before she's finished learning the schottische.
She grabbed Mighty Adolf around the waist, and before anyone knew what was happening she had thrown him on the mat. (7.66)
Strongest Man in the World, meet Strongest Girl in the World. And don't ever underestimate her, or any of her sister-friends, again.
"Fooling, fooling, too much fooling," said Pippi and lifted Thunder-Karlsson up on the wardrobe. A moment later she had Bloom up there, too. Then the tramps were frightened; they began to see that Pippi was no ordinary girl. (8.44)
It's interesting that Pippi never uses her physical superiority to harm anyone, not even a couple of thieves who were clearly okay with stealing from her. She could kick some serious butt if she wanted to, but like Wonder Woman—whose big weapon is a lasso of truth—Pippi is more interested in reform than revenge.
Nearby a house was being repaired, and Pippi ran over and got a long board. She took the board in one hand, ran to the tree, grasped the rope in her free hand, and braced her feet against the trunk of the tree. Quickly and nimbly she climbed up the trunk, and the people stopped crying in astonishment. (10.27)
If there's one scene in the book where Pippi behaves like a true superhero, this is it. She rushes in to do the impossible, and it's a feat that requires not just her superior strength but also agility and problem solving. It also shows that Pippi is mentally strong because of the way she keeps her cool while the rest of the crowd is freaking out.