The irony of Murat's allegiance
Murat's allegiance is first to his family and then to his community, but ironically, he ends up siding with the Russians, because his community has put his family in danger. In other words, because Murat is truly loyal to his wife and children, he cannot be loyal to Shamil's authority, or anyone's. He will always do what is best for his family.
The irony of praise
In this novel, everyone praises Murat. The Caucasians praise Murat, the Muslims praise Murat, and even the Russians praise Murat. But that's not a good thing, necessarily. Because Murat is obviously powerful and glorious, he is an obvious target, and he doesn't survive very long at all. Ironically, praise implies negative attention too, since some people view power as a competition. In other words, he is praised, but also punished for his strength.
The irony of power
Power is ironic in this book, since it doesn't work and it doesn't protect anyone from danger. This is fully represented in the descriptions of the Russian Tsar, a generally despicable person with a nasty habit of mistreating women. But that doesn't mean that Murat respects his own leaders either, and the main conflict of the drama, the conflict between Murat and Shamil, comes from this issue. Shamil doesn't command Murat's respect either.
Chernyshov's betrayal
When Chernyshov claims that Murat is a spy, that makes them mishandle Murat, instead of working with him as they had planned. Instead of honoring their word, the Russians arrest and contain him, which only makes him escape (an ironic effect). He gets a chance to die fighting for his own side, protecting his family.
The epilogue
When we suddenly skip the climax of the story, that's ironic, because it seems that the reader should experience the battle through narrative, but instead, we learn about it in a flashback from the soldiers who are holding his severed head. The end is ironic in other ways too, like that Murat dies fighting against the Russians, as he was in the beginning, which makes the rising action of the novel ironic, since it looks like Murat will work with the Russians.
