15 is too many... It leads to generalizing. Think smaller, both in terms of battles and the number.
As an example, there were no less than 8 major engagements during the Battle of the Bulge. Each distinct and vital to Germany's success or failure. I'll discuss the most important of these later, and it was not the defense of Bastogne.
I will select three "top" battles. These are all overlooked, but very important in more than a few aspects.
The three most amazing battles in my mind would have to include the following: The engagement off of Samar, where the might of Japan's surface fleet was defeated by a tiny force of Destroyers, DEs and CVEs. This was the most incredible naval victory of the war. It was the literal end of Japanese sea power, and established that the U.S. Navy had grown into the most proficient naval power on earth. Go find a copy of "The Last Stand of the Tin Can Sailors" by James Hornfischer.
The defense of Wake Island is second in my opinion. In every way, this was a serious defeat for Japan, despite occupying the island. Had the Navy commander not surrendered the garrison when he did, the remaining Japanese troops on Wake may have been driven into the sea. It's doubtful that the Japanese reserves would have been sufficient to reverse that situation and Japan would have suffered a second great humiliation in their attempt to capture Wake. No doubt they would have eventually prevailed. Yet, a defeat of that magnitude, that early in the war would have shaken the military's confidence and undermined their assumption that Americans were soft and unwilling to sacrifice.
Get a copy of "Given Up for Dead: America's Heroic Stand at Wake Island" by Bill Sloan.
My last choice would be the defense of St.Vith, during the early days of the Battle of the Bulge. The remarkable and stubborn defense of this town completely unraveled the German time table. No other engagement during the Bulge did more harm to the German plan than the defense of this little village. Eventually, the American forces were withdrawn, but the damage was already done. The north shoulder of the Bulge was secured and the entire German effort was trashed.
A great story comes out of this fight, or should I say the withdrawal. The son of American humorist Will Rogers (Will Rogers Jr.) was leading a small column of vehicles out of St. Vith. A few miles northwest, Rogers' Sherman rolled around a bend to a cross roads and came upon a lone GI digging a foxhole alongside the road. The soldier's 2.5" bazooka was resting against a tree. Stopping the tank, Rogers asked what unit the GI was with.
"I'm the 82nd Airborne", said the soldier, "and this is as far as those bastards are going."
Rogers chuckled and called down to the tank's driver. "Pull in behind that guy, we'll make our stand here."
For the record, that WAS as far as those bastards got.
My regards,
Widewing