Immink began climbing in the Dolomites shortly after moving to Switzerland. She made her first major climb in 1889 as she ascended a new route on the Ortler in South Tyrol with a guide. The same year, she made the first female ascent of the Antelao. In 1891 she ascended the Schmitt Chimney of Fünffingerspitze in the Langkofel Group, a year after Robert-Hans Schmitt made the first ascent and expressed doubt that the route would ever be climbed again. She climbed an as-yet unnamed and unclimbed mountain in the Dolomites in 1891 which has since been named the Cima Immink. In 1893, German climber and photographer Theodor Wundt asked Immink if she would accompany him on an ascent of the Kleine Zinne (Cima Piccola) of the Tre Cime di Lavaredo; his photographs of her were later published in his book Wanderungen in den Ampezzaner Dolomiten. This would be her final expedition before she retired from climbing in 1894, having sustained an injury from a previous trip.