What is the will of Zeus in the lliad?

In the Iliad, Zeus is conspiring with Achilles and helping the Trojans, essentially trying to aid in the destruction of the Greeks. Early in the poem, Achilles prays to his mother, asking her to implore aid from Zeus. His wish, which Zeus grants and attempts to carry out, is that Zeus would bring the Greeks to near destruction without Achilles. In this way, the Greeks would see how much they need Achilles to fight for them.
Achilles was a powerful general, and Agamemnon turned against him by refusing to settle the issue at hand—returning the captive woman Chryseis to her father in Troy. When Achilles finally convinced Agamemnon that they needed to return her, he took another woman captive as his spoils: Briseis, the woman Achilles had taken. This action enrages Achilles, and he and his contingent turn and leave in anger. It is at this point that he beseeches the help of Zeus, imploring him to nearly destroy the Greeks so that he can return and be their savior, showing how much they need him.
Throughout the rest of the story, Zeus works tirelessly for this goal, (in his conceit and power) wanting to prove that Achilles is a strong warrior so that he can claim Achilles's deeds as his own work. Zeus encourages Agamemnon repeatedly to join in the fighting, even though multiple truces and deals are made by both sides (pausing the fighting to burn the dead or accepting a deal based on the outcome of a duel). The end result of each of these pauses is Zeus reigniting the bloodlust in Agamemnon so his men will fight and fail.
Late in the story, after being seduced and falling into a slumber, Zeus fails to stop the other gods from intervening. Enraged, he sends Apollo, the God of War, to aid the Trojans. His vitriol and fervor eventually succeed, weakening the Greeks to the point where they will give Achilles whatever he desires. When he returns, Zeus allows the gods to choose sides and enter the fray while Achilles goes to work conquering the Trojans in earnest.
Zeus desired to help Achilles, but this was mainly because he knew that his own fame and power would grow because Achilles would be successful. If he could claim Achilles as his supporter and follower, he would gain more devotion and therefore strength, because Achilles was a powerful general and fighter. So, in the story, his will was to bring the Greek army low so that Achilles could save them.