When I came in to send this I noticed Grace had posted - hey Grace I like your version of Rimmugýgi. I saw it slightly differently
Well here we go - very nice fair fight good on ya Skarpheðin
 
45. kafli

Nú er að segja frá Njálssonum að þeir fóru upp til Fljótshlíðar og voru um
nóttina við hlíðina og fóru nær Hlíðarenda er morgna tók.
Now it is to tell of Njal's Sons as they journeyed up to Fljotshlið and were there over night, on the slope and went to Hliðarend when morning came
 
Þenna morgun hinn
sama stóðu þeir upp snemma, Sigmundur og Skjöldur, og ætluðu til stóðhrossa.
That same morning they got up early, Sigmund and Skjold and intended to  (look for - see to ) a Studhorse

Þeir höfðu beisl með sér og tóku hross í túni og riðu í braut.
They had bridles (tack) with them and took two horses from  the home meadow and rode out (away from home)
 
Þeir leita
stóðhestsins um hlíðina og fundu hann meðal lækja tveggja og leiddu hrossin
ofan að götum mjög.
They saw the Stallion on a slope and found him between two brooks and brought the horse down to a good road (? a wider road for safety)
 
Skarphéðinn sá Sigmund því að hann var í litklæðum.
Skarpheðid saw Sigmund - he was in bright clothing

Skarphéðinn mælti: "Sjáið þér rauðálfinn sveinar?"
Skarpheðin spoke "Do you see the red elf Lads?"

Þeir litu til og kváðust sjá hann.
They looked and declared themselves able to see him

Þá mælti Skarphéðinn: "Þú skalt gera að ekki Höskuldur því að þú munt oft
sendur einn saman óvarlega.
Then spoke Skarpheðin " Hoskuld - you shall do nothing because you must often travel alone and unprotected -
 
 En eg ætla mér Sigmund. Þykir mér það karlmannlegt.
but I choose Sigmund for myself. I think to myself that is a man's work. (i.e. not the job for a boy
 
En þið Grímur og Helgi skuluð vega að Skildi."
But you  Grim and Helgi should kill/take-on Skjold"

Höskuldur settist niður en þeir gengu þar til er þeir komu að þeim.
Hoskuld sat himself down (for to mind the horses perhaps) and they (the others) walked on over till they came to them (Sigmund and Skjold)

Skarphéðinn mælti til Sigmundar: "Tak vopn þín og ver þig. Er það nú meiri
nauðsyn en kveða flím um oss bræður."
Skarpheðin spoke to Sigmund "Take up your weapons and cover/defend yourself.
It is that now you need more than reciting mockery/jokes of us brothers"

Sigmundur tók vopn sín en Skarphéðinn beið meðan.
Sigmund took his weapons and Skarpheðin waited meanwhile (fair fight )
 
Skjöldur sneri í mót þeim
Grími og Helga og börðust þeir í ákafa.
Skjold turned to them Grim and Helgi and they fought together furiously
 
Sigmundur hafði hjálm á höfði sér og
skjöld á hlið og gyrður sverði og hafði spjót í hendi, snýr nú í mót
Sigmund had a helmet on his head and a shield at his side and was girt with a sword (well - stuck in his belt) and in his hand a spear - he turned to meet -
Skarphéðni og leggur þegar spjótinu til hans og kemur í skjöldinn.
Skarpheðin  and thrust at once with his spear and it came (hit upon) his (Skarp's shield)

Skarphéðinn laust í sundur spjótskaftið og færir upp öxina í annað sinn og
höggur til Sigmundar og kom í skjöldinn og klauf ofan öðrum megin mundriða.
Skarpheðin struck asunder (cut right off) the spearchaft and got (G) up his axe  again and  sliced/hewed at Sigmund and came to (landed in) the shield and split it to the hand-grip.

Sigmundur brá sverðinu hinni hægri hendi og höggur til Skarphéðins og kom í
skjöldinn og festi sverðið í skildinum.
Sigmund drew his sword with his right hand and struck at Skarpheðin and came into the (Skarp's) shield stuck fast the sword into the shield
 
Skarphéðinn snaraði svo fast  skjöldinn að Sigmundur lét laust sverðið.
Skarpheðin turned (? twisted) so quickly - his shield that Sigmund let go his sword
 
Skarphéðinn hjó þá enn til
Sigmundar með öxinni Rimmugýgi.
Skarpheðin sliced then again at Sigmund with his axe Battle-Ogre (or demon ?)
 
Sigmundur var í pansara.
Sigmund was in a leather belt (?cuirass)  CV gives this as panzara
 
Öxin kom á öxlina
og klauf ofan herðarblaðið.
The axe struck his shoulder and split (down to) the shoulderblade
 
Hann hnykkir að sér öxinni og féll Sigmundur á
kné bæði og spratt upp þegar.
He (Skarpheðin) pulled the axe towards himself and Sigmund fell to both knees but sprang up at once
 
I have recognised a total difference between Skarp & Co the Neilsons - they are of a different metal from the others - to allow an enemy to arm himself for battle would not be the way of Sigmund and Friends
I have used cuirass for what Sigmund was wearing - I think in Zoega you have a choice  and chainmail might have just deflected a glancing blow from an axe but the leather is only proof against a sword IMHO
Skarpheðin is a great guy - who cares what he looks like he fights well and honourably
Kveðja
Patricia