Here’s my translation

Alan

Ok skyldi ek þess grimmliga hefna ef ek gæta náð honum.”
And I should avenge that fiercely (‘take a fearful revenge for that’, Z) if I were-able (geta + pp, subjunctive) to get-hold-of (pp of ná) him.“

Verðr nökkvinn nú landfastr.
Now the-boat reaches land (lit: becomes ‘land-fast’).

Hljóp jötunninn nú fyrir borð.
The-giant leapt now over-board.

Knútr kom þar fram á bakkann.
Knútr comes there forward on to the-bank (of the vatn, lake).

Jötunninn var óða málugr.
The-giant was speaking violently (presumably óða málugr = óð-málugr, Z).

Knútr tók upp stein ok snaraði til hans, ok kom við eyra honum.
Knútr took up a stone and throws (snara, Z4) (it) towards him, and (it, the stone) came against his ear (gave him a whack on the ear).

Hann hristi við höfuðit ok mælti “hvasst er nú á hömrunum svá feykir vindrinn fjöðrunum.”
He (ie the giant) shook with the-(his) head and spoke “(It) is fresh (breezy) now on the crags such (that) the-wind blows with feathers (ie the breeze is now sufficiently fresh to whip up loose feathers, one of which just brushed against my ear)”

Tók hann þá gaddakylfu, járnvafða, ok hljóp neðan einstigit.
He took then a club-with-spikes, iron-wound (woven), and ran from-below (ie up) the-narrow-(ascending)-path (cf stigi = ladder rather than stigr = path).

Hálfþrítugr var hamarrinn.
Twenty-five (fathoms high) (lit: Half-thirty, see hamarr, Z3) was the crag.

En þá er hann var kominn í it efsta stigit, renndi Knútr at honum ok rak spjótit fyrir brjóst honum.
But (And) when he was (had) come into the uppermost step, (stig) Knútr ran at him, and drove the-spear through (lit: before) his breast.

Spjótit gekk á kaf, en jötunninn datt ofan fyrir hamarinn ok brotnaði í honum hvert bein.
The-spear went into (the) water, but (and) the-giant fell down over the-crag and every bone (nominative) was-broken in him.

En Knútr tók kylfuna til sín en síðan sté hann á nökkvann ok reri til eyjarinnar, gekk á land ok litaðist um.
But (And) Knútr took the-club for himself but (and) after-that he stepped onto the-boat and rowed toward the-island (fem gen sg), went on-to land (ie ashore) and looked-about.

Hann sá hól einn háfan með fögrum grösum.
He saw a single knoll high (háfan = masc acc sg of hár) with fair grasses (herbage, plural).

Þangat gengr hann.
He goes (on foot) thither.

Hann finnr þar á glugg; hann setr gler fyrir augu sér.
He finds there a window (opening); he sets (the) glass (of the window) before his eye (ie he brings his eye up to the glass of the window).

Hann sér hvar krákan lá á mikilli dyngju.
He sees where the-crow lay on a great lady’s-bower.

Hann sá af henni var vængrinn.
He saw the wing was off (from) her (ie missing, sans wing)

Hann tók þá í posa kerlingar ok sáði inn í glugginn því sem þar var í.
He reached (taka, Z3) then into (the) little-bag of (the) old-woman and scattered inside in the-window that which was in (it, the bag) (presumably having opened the window first)

Fell þá svefn á krákuna.
Then a sleep fell on (descended upon) the-crow.

En síðan fór hann inn í hólinn.
But (And) after-that he ventured inside into the-knoll.

Hann tók um háls krákunni ok snaraði hana úr hálsliðnum í millum handa sér en í hennar fjörbrotum varð svá mikill landsskjálfti at undrum gegndi.
He took-hold of the-neck of the-crow and twisted her (ie kráka, Hlégerðr: as this is fem it can’t refer to háls which is masc) out-of the-neck-joint between his hands but (and) (the) land-shivering (earth-trembling, earthquake) became so great in her death-struggle that (it) amounted to wonders (plural) (ie was truly amazing, beyond earth shattering).

13
13

Knútr tekr sér nú eld ok gekk til dyngju krákunar ok rubbar henni upp allri.
Knútr strikes (see taka eld under eldr, Z) for himself now a fire (I´m guessing as a torch) and went (on foot) to (the) lady’s-bower of the-crow and huddles (rubba, CV) it (the bower) all up (presumably turns the place upside down in his search).

Finnur hann eggit ok lætr þat koma í posa kerlingar.
He finds the-egg and causes that to come into (the) small-bag of (the) old-woman.

Niðri undir dyngjunni fann hann jarðhús.
Further-down under the-lady’s-bower he finds an underground-room.

Þar lá fyrir ormr einn.
There a single serpent lay in-front-of (it).

Hann bles þegar eitri ok sakaði Knút ekki fyrir taufrum kerlingar.
He (it, the serpent) blew at-once venom and harmed Knútr not, because of (the) charms (of the sorcery type, not the saucy) of (the) old-woman.

Ormrinn fló út um glugginn.
The-serpent flew out through the-window (luckily Knútr had left it open, otherwise glass would have gone everywhere).

Gull mikit ok gersimar var þar.
Much gold and treasures were there.

Hann fylldi upp uxahornit.
He filled up the-ox-horn (you never know when an ox-horn will come in handy – Knútr obviously knew that)

Tók hann þat af gullinu sem honum likaði.
He took that (selection) of the-gold which pleased him.

Vendi hann síðan í burtu.
He turned away after-that.

Kemr hann nú til nökkvans ok rær síðan at landi.
He comes now to the-boat and rows after-that to land (ie the shore of mainland)

En er kemr á vatnit þá kemr ormrinn upp úr vatninu með gapanda munni ok leggst at nökkvanum ok lagði bægslit upp á barðit.
But (And) (apparently almost before he’d got started) when he comes on to the-lake the-serpent comes up out-of the-water (lake) with gaping mouth and lays-himself (itself) against the-boat and placed the-(his, its) shoulder (boexl, Z, bægsli, MnI Dictionary = flipper) up on to the-prow.