I don't think anybody needs to worry about spoilers for The Northman in this post being that most of what I'm talking about is in the trailer or in a few reviews; but, I don't know, read at your own risk.
The film (and, yes, it was shot on film) has rightly drawn a lot of comparisons to Hamlet. The film is based upon the Scandinavian story of Prince Amleth which directly inspired Shakespeare. Still, a lot of people have been going too far by simply saying, "It's Hamlet in medieval Iceland." I read Hamlet once a year and I have since high school; so, the overly simplified comparisons bother me.
Yes, the story of a prince seeking revenge against an uncle who killed his father, usurped the crown, and married the queen is identical to Hamlet. Still, this is a very different story.
It's shown in the trailer that Amleth witnesses his father's assassination; so, obviously, there's no story like the one in Hamlet about doubting the guilt of his uncle. There's no act 2 scene 2 soliloquy needed here.
Basically the first act of The Northman has significant crossover with the first three scenes of Hamlet with important differences. The second and third acts of The Northman are what I think Shakespeare might have written after act 4 scene 4 of Hamlet if he had decided to keep the focus on Hamlet rather than having several scenes without him while he was away in England.
So, yes, the set up and the inciting incident have a lot in common with Hamlet. Otherwise, most of The Northman was dealing with the aspects of the story that Shakespeare left out.