The opening sentence (the first three lines) has niggled at me, but I came up with good solutions for two thirds of it.
The fighting Danes of former days,
the kings of the nation, we know their fame...
I have had the following line read
and how they earned honour through deeds.
The line sounds good, I think, but does not perfectly render the original meaning, which means something along the lines of
and how those lords exploits accomplished.
I can come closer with
and the proud deeds those princes did.
This is a good place to explain how and why I am breaking the rules of Alliterative Verse from time to time. Old English verse never has the two stresses of a half-line together at the end, as I just put them in "and the PROUD DEEDS." However, for many lines in Beowulf, that is the simplest and most accurate way to translate. For example, "in the beer hall," "in the gold hall," "in the wine hall" all work beautifully in Old English because the words for the hall--sele, reced--have two syllables. Not so in modern English. A way around the problem is to create lines like "in the hall of gold," but that is awkward and misleading. The gold hall fairly clearly means the place where gold is given out, not the place that is made of gold; after all, the wine hall is where wine is given out...it does not mean that the hall is made of wine! I could use a different word, such as mansion or palace. In the end, I sometimes used hall even though it meant that some few half-lines had their two stresses together at the end.
P.S. On the other hand, I can avoid breaking the rules with this:
and the proud exploits those princes did.