In WW II, which Allied fighting unit scaled a 1,500 ft.-vertical-mountain side to attack and defeat a German Army Unit. (The Germans considered the ridge to be impossible to scale.) :

The U.S Army 10th Mountain Division entered combat on January 28, 1945 in the North Apennine Mountains of Italy. The division faced German positions arrayed along the 5 mile long Monte Belvedere-Monte della Torraccia ridge. Other divisions had attempted to assault Mount Belvedere three times, even holding it temporarily, but none had succeeded. To get to Mount Belvedere the division first had to take a ridge line to the west known to the Americans as the Riva Ridge. The Germans on Riva Ridge protected the approaches to Mount Belvedere. The assault on Riva Ridge was the task of the 1st Battalion and F Company, 2d Battalion, 86th Mountain Infantry. After much scouting, it was decided the assault would be at night, a 1,500-vertical-assent. The Germans considered the ridge to be impossible to scale and manned it with only one battalion of mountain troops. The attack by the 86th on February 18, 1945, was a complete success and an unwelcome surprise to the Germans.

Mount Belvedere was assaulted next. Belvedere was heavily manned and protected with minefields. Shortly after the 86th assault on the Riva Ridge, the 85th and 87th Regiments made a bayonet attack without covering artillery fire on Belvedere beginning on February 19th. Again the surprise of the assault was successful and after a hard fight, the peak was captured. Realizing the importance of the peak, the Germans made seven counterattacks over two days.