So the first Ivan Groznyy came out in 1944 and the second part didn't come out until 1958. That's a long time to wait for a sequel!
So there's more government problems and more stuff to worry about for Ivan in this film. We also learn more about his past, that his mother was poisoned by the boyars. We know this because she shouts poison really loudly. Thanks for the exposition, Ivan's mom.
Ivan also learns that Big hat lady was responsible for poisoning his beloved wife, and vows revenge. Big hat lady wants her son to rule as tsar. Or, since he's a giant man child, she would do most of the actual decision making.
Ivan proves he's a pretty clever guy. He invites Vladimir, the man-child over to watch a play and drink with him. Vladimir tells him about certain people wanting his reign to end, so Ivan gives him his crown and lets him play pretend tsar for awhile. While doing so, an assassin kills him, thinking that he's the real tsar. His mom comes in joyous that Ivan has been destroyed, only to realize her own son was killed. Ivan announces that he won't punish the assassin, for he has killed his enemy. And that's it, it's a really short film.
Ivan does do some talk about his power being derived and strengthened by the people, but we know that was really Stalin talking. This was less like a silent film than the first, but it still wasn't any better. I will give it a 5/10.