What is the irony in Rimbaud's "Barbarian?"
When a work is truly ironic, it often contains more than one instance of irony, or is ironic at more than one place.
The first way that this poem is ironic is that it is a poem. True barbarians have only minimal art.
The second way this is ironic is closely related: this poem is highly sophisticated. It is anything but barbarian. Look at the repetition and the imagery: very sophisticated, and not barbarian or savage.
Now, move to more specifics: look at the subtle concepts contained in the images and metaphors. Some of these are ironic. Look at lines like "arctic flowers." This is an impossibility, a kind of irony. Likewise, the "wind of diamonds" is impossible. Diamonds are very hard and sparkle with visibility. Wind is invisible. The result is both linguistic and situational irony.