Admiral Halsey (US Navy) commanded at the Battle of Leyte Gulf during WW II. It was a great US victory, but almost turned into a disaster as Halsey's forces were left open to ambush. Evaluate Halsey's leadership during this battle.

This is a very complicated question, and one which demands you exercise your own judgment, as to the degree to which Halsey deserves condemnation for his failings during the Battle of Leyte Gulf. In any case, here some general considerations I suggest you keep in mind: war is very, very messy, and decisions are made off of imperfect intelligence, at the highest of stakes and pressure, and contingency always plays a critical role in how events play out. Additionally, one should also always keep in mind the strategic considerations in any given operation: what are the underlying objectives behind any given actions? I think, before you try to pass any kind of evaluation, you would do well to keep these general considerations in mind.
I can't actually give you an evaluation of Halsey's competence (that is probably best left up to your own judgment), but I can give a general overview of just what happened at the Battle of Leyte Gulf and the implications which Leyte's decision-making entailed.
First, keep in mind, again, the military context of this battle, as part of Douglas MacArthur's island-hopping campaign, by which the United States moved from island to island across the Pacific, pushing the Japanese further back, in order to eventually close in on Japan. The stakes were high, and the Japanese regarded this attack on the Philippines "as a crisis of the war. Its generals recognized that, if the Philippines were occupied by the Americans, the supply lines of the Japanese Empire would be fatally obstructed" (Peter Calvocoressi, Guy Wint, & John Pritchard, The Penguin History of the Second World War, England: Penguin Books, 1999 reissuing, 1154).
This represented a joint operation between the US army (led by MacArthur) and its navy. The Japanese responded by way of a diversion. Seeing what he assumed was the Japanese fleet in retreat, Halsey fell for the deception, taking the entirety of his forces to follow in pursuit, with the intention of destroying the enemy fleet. In the process, however, he left US landing operations vulnerable to Japanese attack. As the Penguin History later notes, this decision could have proven devastating to US operations in the Pacific theater, given that the Japanese fleet actually did break through the American naval defenses, noting that:

The larger Japanese fleet . . . got through the American defenses, and for a time, if it had but known this, had the American transports at its mercy, but because of the muddle . . . and because of deep misunderstanding of what was being done by the American ships, the Japanese Admiral did not bombard but sailed away inexplicably. (1157)

Here we see the role of contingency, as what could have been a disaster became a victory instead. There's definitely room to criticize Halsey's decision-making, especially given the strategic priorities, but it might be worth also considering, as best as one is able, the strategic limitations and constraints which were placed upon him as well: the intelligence he may have had available to him and his own reading of the situation in question. It's easy to level criticism from the outside. In any case, those same historians I've quoted before also provide him some measure of defense, stating that despite the criticisms leveled against him, "given the system of communication prevailing among the warships, he could hardly have done other than he did" (1157).