Why this show failed...
First, they shouldn't have called it Beowulf. What's wrong with "Return to the Shieldlands"?
It had so much potential, a great setting and decent production values/SFX. The acting was good enough for a series like this as well and it had a well balanced cast.
But why did it fail? Like so many shows like it, it was the story and it was the writing. And it's such a pity because the potential for great stories certainly was there. The personal struggle of "Beowulf" (again, should have called him something else), the whole mud born mythology and Elvina, the economic and political situation of the Shieldlands, even the sub stories of the honest thief, woman blacksmith and the other townspeople could have had something to it.
Unfortunately there just wasn't a concise story arc. Episodes seemed centered around the fight scene of the week and fight scenes are very hard to do. They should be sparse, special and epic. All these poorly choreographed, confusing, amateuristic battles with nothing at stake dragged the whole show down. The rest of the storytelling in the end wasn't all that interesting either. Cliched dialogue, monotonous performances, it just took itself too seriously.
The Last Kingdom is a show that does get all this right, still there's too few shows in this genre (although due to the success of GoT we have seen an increase) so it's still a pity this doesn't get the chance to learn from their mistakes in a season two.