In August 1857, Kaufmann participated in the first ascent of the Mönch. In July 1856, the Viennese physician Sigmund Porges had climbed the Jungfrau with the Grindelwald guide Christian Almer. The next year he came back to attempt a first ascent of the notorious Eiger. Christian Almer was Ulrich Kaufmann's brother in law, possibly explaining how Porges included the 17-year old Kaufmann as one of his guides, along with Almer and Christian Kaufmann Sr. They took off on August 13, but conditions were poor. The attempt on Eiger faltered the next day, and the party turned its attention to the neighboring Mönch. They had another bivouac an hour below the Mönchjoch and finally summited Mönch at 3 pm on August 15, after Kaufmann and his fellow guides had cut 300 steps in ice. The next year, Porges performed the second ascent of Eiger with different guides. In 1882, Kaufmann undertook the first attempted ascent of Aoraki / Mount Cook with William Spotswood Green, and Swiss alpinist and hotelier Emil Boss. On 2 March 1882, they failed just short of the summit because of a storm. The first complete ascent of Aoraki would not take place until nearly 13 years later. In 1883, he and Emil Boss took part in the first climbing expedition in the Himalayas, led by William Woodman Graham. Among others, they claimed a near ascent of Dunagiri and an ascent of Changabang in July in the Garhwal Himalaya. These claims are widely disputed and were probably based on poor maps and a misunderstanding of their location. However, their ascent to 30 feet below the east summit of Kabru south of Kangchenjunga in October of that year is now considered quite likely. Before this time, no one is known to have reached over, though it is possible that Incas reached the summit of Aconcagua in Pre-Columbian times. Kaufmann, Boss and Graham therefore likely broke the world altitude record in mountaineering by 350 m or 550 m and held this record for 26 years, until the Duke of the Abruzzi's expedition to the Karakoram in 1909 reached an altitude of ca..