Not quite "physically strong" but competent and courageous
I've always been a big fan of Thuvia from The Gods of Mars. She was kind of the odd woman out among the women of that story, compared to Deja Thoris, the damsel in distress, and Phaidor, the woman who loves John Carter but is really a bad guy. Thuvia just kind of is there as a sidekick, and I suppose she's supposed to love John Carter also (who doesn't!) but she doesn't really fit into any love triangles.
In any case, Thuvia subdues some banths, great beasts that would likely have overpowered the Hero (John Carter) and Sidekick (Tars Tarkas):
As I was about to spring into the conflict with my sharp long-sword I
felt a gentle hand upon my shoulder and turning found, to my surprise,
that the young woman had followed me into the chamber.
whispered, "leave them to me," and pushing me advanced, all
defenceless and unarmed, upon the snarling banths. When quite close to
them she spoke a single Martian word in low but peremptory tones.
Like lightning the great beasts wheeled upon her, and I looked to see
her torn to pieces before I could reach her side, but instead the
creatures slunk to her feet like puppies that expect a merited
Incidentally, she did this from a power inherent to her, not because of some magic or trinkets
"When first I came here I angered Sator Throg, because I repulsed him.
He ordered me to be thrown into one of the great pits in the inner
gardens. It was filled with banths. In my own country I had been
accustomed to command. Something in my voice, I do not know what,
cowed the beasts as they sprang to attack me.
"Instead of tearing me to pieces, as Sator Throg had desired, they
fawned at my feet.
She generally provided all the brain-power necessary for the escape from the Therns in the first part of the book, as well as a lot of the muscle through her banths. She also killed said Sator Throg, her slave owner, without much of a spare thought:
"Stop!" he cried. "What means this, Thuvia?"
For answer the girl raised her revolver and fired point-blank at him.
Without a sound he sank to the earth, dead.
"Beast!" she hissed. "After all these years I am at last revenged."
Gods of Mars ended on a cliffhanger ending with Phaidor seemingly killing Deja Thoris, but in the sequel The Warlord of Mars we learn that
Thuvia had wrested the blade from the daughter of Matai Shang
[Phaidor] before it had touched either Dejah Thoris or herself.
Of course by this point, Thuvia had been swept up alongside Deja Thoris as perpetual damsel in distress, a role she continued as damsel-in-chief of the next book, Thuvia, Maid of Mars. But for a while, at least, Thuvia was portrayed as a tough, competent sidekick.