First of all, please note that “war” is not the correct term to use here. Hitler only led Germany during one war. This war was World War II. It would not make sense to ask what war contained Hitler’s final offensive. The term you probably want to use here is “battle.” A battle is a single incident within a larger war. If this is what you are really trying to ask, the answer is Operation Spring Awakening, also known as the Lake Balaton Offensive. The Battle of the Bulge is more famous as Germany’s “last gasp,” but Operation Spring Awakening actually occurred later.
As its name implies this battle was fought near Lake Balaton in Hungary. It happened during March of 1945. By this time, the Soviet army was advancing towards Germany. The Lake Balaton Offensive was meant to halt this advance. The German army planned to break through Soviet lines and then encircle two of the Soviet armies. However, the Germans did not have enough troops and the troops that they had were not strong enough (many had been in the Battle of the Bulge not long before) to actually succeed. The Soviets defeated the German offensive and the war ended about two months later.
WWII in Europe was a two fronted war, i.e., the Western Front and the Eastern Front. In other words, the war for Hitler was two wars at once. To win he had to win on both fronts and to clearly defeat Hitler, the Allies had to defeat him on both fronts. The Ardennes Offensive (more commonly known as the Battle of the Bulge), that ensued December 16, 1944, and ended January 25, 1945, was Hitler’s last offensive on the Western Front. This is considered by some, Winston Churchill included, to have been greatest battle fought by the Americans in World War II. It was one of the biggest battles of the war and, if General George S. Patton had not been able to intervene with his Third Army, all would have been lost to Hitler.
Hitler’s later offensive (March 6,1945) on the Eastern Front, Operation Spring Awakening, was Hitler’s last, futile effort to halt Allied advances into Germany. It was quite literally Hitler’s last stand. He likely knew it was futile since he’d already lost the Western Front. He sent his own elite army, the 1st SS Panzer Unit, to confront the Soviet Red Army at Lake Balaton in Hungary. Just 10 days later (March 16), Hitler’s elite army was in retreat from the Soviet counter-offensive. Hitler was furious at the 1st SS Panzer Unit’s retreat and stripped them of their armbands bearing his own name. It was Hitler’s last major offensive of the war and, only 6 weeks later — April 30, 1945, Hitler committed suicide.
It is imperative to note that without the defeat of Hitler at the Battle of the Bulge, the final offensive at Lake Balaton would not have been concocted by Hitler. He failed to stop the Americans and British in the West and needed a victory, but more importantly he needed preserve some resources for negotiating the terms of surrender, hence the failed, last ditch effort in the East.