In my opinion, the climax of the Iliad comes in Book 22. I think that the climax comes when Achilles kills Hector. The reason that I say this is because this is the apex of the rage of Achilles.
I think that much of the point of this epic is the anger of Achilles. After all, the poem starts by asking the goddess to sing of the wrath of Achilles. We see Achilles' anger cause him to withdraw from the war and sulk in his tent because his pride has been offended. Later, we see his anger cause him to fly into a murderous rage as he takes revenge for the death of Patroclus (which was caused, you can argue) by Achilles' anger.
So the whole epic is about the consequences of Achilles' anger. This anger peaks as Achilles kills Hector and gets his revenge. After that, the rest of the epic is really just about tying up loose ends caused by Achilles' anger.