The Firebird
Ironically, it is revealed that The Firebird is not actually the amplifier. This was entirely unexpected, as Alina was sure The Firebird could help her.
The Darkling
The Darkling's love for Alina is quite ironic. This is because he claims to love her, but destroys everything she loves and kills her friends.
The Priestguards
Alina describes how the Priestguards "wore the golden sunburst," but they ironically won't look at Alina. This is ironic because she is the Sun Summoner.
Irony of rats
Rats are usually presented as undesirable creatures, which is something Alina alludes to when she compares herself to a "rat in the warren." However, The Apparat actually shows that there is ironically a good time to be a rat, which is during "times of trouble."
The amplifier
Alina spends the majority of the novel looking for The Firebird, who promises to give her strength. However, the whole time it is actually Mal who is the amplifier. This is ironic because she didn't actually have to do all that searching in the end.