I'm pretty sure this is "The Intruders" (1964) by Robert Rohrer, published in Amazing Stories, October 1964. The only missing point is that it wasn't ever anthologized, it was only ever republished in Thrilling Science Fiction, February 1973. You can read the story at the Internet Archive.
The viewpoint character is a spaceman named Harley who has gone space-mad and killed his partner MacMahon:
He still hadn't been able to find the monster MacMahon had been talking about over the radio. Harley had been crouching in the companionway below the control room, watching MacMahon. He had heard MacMahon say, "...a monster, I tell you, a monster. I can't find him anywhere.... No, he still has it.... All right, I'll try to. Out." MacMahon had turned from the radio, clutching to his stomach the hand Harley had hit with the meat cleaver. Then Harley had entered the control room, and MacMahon had tried to force him into the vault, and Harley had put MacMahon 'tween hulls.
A ship docks to his to retrieve him, but in his delusion he thinks he is being attacked by monsters:
There. There, in the lower left corner of the viewport, if he craned his neck, he could see the tail fin of another ship.
And then realization hit him. The monster had escaped, and it had brought back several of its comrades. They were going to blast in and destroy the ship. They were going to...
Four astronauts come aboard to check on things, but Harley is in hiding and MacMahon's body is hidden between the hulls. Not expecting a murderer, the astronauts split up to search the ship. Harley kills one who is searching a storage compartment, and the others realize he is using the ventilation system or the inter-hull space to move around and go after him.
"Watch for Lieutenant Harley. He's trying to pick us off singly. He’s either going from room to room through the ventilation system or by the girders 'tween hulls. Lindstrom and I are going to look for him together."
But this is a trick by Harley; he decoys them down into the inter-hull space by dropping his shoes, then kills the fourth astronaut to take control of the command chair. He the initiates a high-g manoeuvre:
The indicator on the panel jumped to 10g. There was a groan as the shock-absorbing girders 'tween hulls yielded slightly to the pressure of the outer shell.
"Captain, I can hardly move!"
"Harley must have gotten to the control room. We've got to get out of here."
Harley heard the two creatures scuttling up the side of the inner hull. At maximum g, the outer hull would be pulled to within two inches of the inner. The indicator needle jumped to 20g then to 30.
"Sir, my foot! It's caught!"
"Can't you get it out?"
"No — no. I can't move."
"Pull on the rope. Pull!"
"Can't—get out—my foot—"
"The outer hull's pressing in. You've got to get free! Harley! Harley, if you can hear me, stop this!"
We won't answer him, ship. He doesn't exist. The needle shot to 40g; the outer hull sank to within three feet of the inner.
"Captaaaaainn! My foot, it's crushed, my foot!"
"Harley, for the love of God, don't do this! We'll take you back to Earth! We'll take you away from this place! You'll be safe! If you stay here much long..."
Then the needle shot up to 50g, and the outer hull snapped to within one foot of the inner. The rest was a confused jumble of crackling bones and screaming.
And sure enough, at the end he's about to run out of air:
Somewhere, far down in the heart of the rocket, there was a hiss as the last tank of compressed air was released into the ventilation system.