From 1753 to 1757 Zingg got a training as a copper engraver under J.R. Holzhalb (1723-1806) in Zurich. Then he worked as an engraver in the studio of J.L. Aberli (1723-1786) in Berne. 1759 he travelled with Aberli and J.E. Mörikofer (1706-1761) to Paris to visit the engraver J.Gg. Wille (1715-1808).
Until 1766 he lived and worked in Paris, except a short stay in Switzerland 1764/65. Supported by Wille he got several commissions to make engravings after C. Vernet (1758-1836), C.G. Schütz (1718-1791), C.W.E. Dietrich (1712-1774) and others.
Already in 1764 the newly founded academy of arts in Dresden under Chr.L. von Hagedorn (1712-1780) offered him a post of a teacher for engraving. He travelled via Bern, Zurich, Augsburg and Nuremberg to Dresden and started his new job in 1766. He became friends with C.W.E. Dietrich und A. Graff (1726-1813). 1769 he became a member of the academy of arts in Vienna, 1787 in Berlin. In 1786 he travelled to Switzerland.
From 1803 he was professor at the academy of arts in Dresden. Already in 1766 he started to go on hikes through the Elbe Sandstone Mountains and especially in the 80th and 90th he walked through the Elbe Sandstone Mountains, the Ore Mountains, the Lusatian Mountains, the aereas around Meissen and Leipzig, through Bohemia, Brandenburg, and Thuringia, where he made many landscape drawings.
In 1804 a series with copper engravings („Adrian Zinggs Kupferstichwerk“) was published by Tauchnitz in Leipzig. Besides that he made several publications for his drawing lessons.