The irony of downfall
One would think that since Moor is the main hero or protagonist of this novel, that he might have some positive associations in his name, but he intentionally includes the story of the fall of the Moors in Granada. In other words, this is a story about a character defined not by his superhuman strength, but by the superhuman awareness of his weaknesses.
The irony of power
Instead of finding his source of power in some kind of ability or power, Moor is shaped by his inability. His bad hand is a symbol for this awareness. It's an ironic superpower to be so weak, you know not to try and control your life. Without the illusion of control, Moor's judgment is more clear.
The irony of time
Moor lives life at twice the speed everyone else does, because he ages twice as fast, which means he grows twice as fast, but it also means that he dies twice as fast. So his life more clearly demonstrates the drama of a human life, the rise from powerlessness to power that comes from accelerated growth, and the epic downfall toward death that comes from Moor's accelerated decay. In this case, the author's decision to play with time is illustrating life's basic irony: that humans die.
The irony of art
Art is both an act of self expression and communication. Ironically, the character who teaches Moor about himself, his family, and his government is his mother who both paints those pictures for Moor metaphorically through parenting, but also literally and physically, because Moor sees her paintings. Then Moor falls in love with another artist, a sculptor, who helps Moor by sculpting his expectations for life. She is too unpredictable and fun and chaotic to possibly be contained by Moor, so she unleashes his imagination, sculpting his experience of life. In this case, art is ironic, because it's self-referential, since the novel itself is an artwork.
The irony of identity
The novel begins on an ironic note when Moor starts telling us about himself without making any references to himself. Instead, he just paints a picture of his ancestry, setting the framework for his life's context. Ironically, his sense of identity isn't one solitary entity, but, rather, Moor views himself as a continuation of the lives of his ancestors. This irony helps him to make sense of his expedited life and death.
