Here is a clip from the makers of the show talking about/showing the scene in question.
I know vikings (and Saxons, too) were fond of the shieldwall. Would they really hold their shields up 3-4 ranks high as depicted in the show?
The short answer is that (1) The Last Kingdom portrays the Danish invasion armies of ca. 890, which would have looked a lot larger and probably also more disciplined then earlier vikings, who were essentially just small bands of raiders; and (2) shield walls were a pretty common tactic throughout the early middle ages, giving Danish armies no real advantage over Anglo-Saxon fyrds, despite the way that the Last Kingdom portrays shield walls as some sort of Norse invention that the Anglo-Saxons needed to adopt.
It seems to me that Alfred's greatest reasons for success might have been dumb luck and his development of towns as sites for rapid mobilization and in-depth defense. Moreover, Alfred benefited from the able pen of Asser, who gave him a larger-than-life legacy and perhaps more credit than was his due. For more, see:
/u/EyeStache's comments on the differences between víkingar and the armies of The Last Kingdom
/u/cazador5's comments on tactics and shield walls in the Viking Age
Richard Abels, Alfred the Great: War, Kingship and Culture in Anglo-Saxon England (1998).
Guy Halsall, Warfare and Society in the Barbarian West, 450–900 (2003).
Ryan Lavelle, *Alfred's Wars: Sources and Interpretations of Anglo-Saxon Warfare in the Viking Age (2010).