Tappy was a member of the Grand Théâtre de Genève from 1962 to 1974, where his wide repertoire included major Mozart roles and world premieres such as Darius Milhaud's La Mère coupable.

He has been regarded as legendary for portraying Monteverdi's Orfeo, Tamino in Mozart's Die Zauberflöte and Debussy's Pelléas,[1] with a voice of exemplary clarity and diction.

[2] He appeared as a guest internationally, in Rameau's Zoroastre in Bordeaux and in Paris, in the title role of Monteverdi's L'Orfeo at the Drottningholm Palace Theatre, and as Nerone in L'incoronazione di Poppea at the Staatsoper Hannover.

[2] After he appeared as Nerone in L'incoronazione di Poppea at the Zürich Opera in 1979, directed by Jean-Pierre Ponnelle and conducted by Nikolaus Harnoncourt, alongside Rachel Yakar in the title role, the production was also shown at the Edinbourg Festival and La Scala in Milan, and was filmed.

He recorded Debussy's Pelléas et Mélisande twice, in 1969 a live recording in Geneva conducted by Jean-Marie Auberson, with Erna Spoorenberg, Gérard Souzay, and the Orchestre de la Suisse Romande, and in 1979 conducted by Armin Jordan, with Yakar, Philippe Huttenlocher, and Chœurs et Orchestre National de L'Opéra Monte Carlo.

A reviewer noted his "fine, lean voice", more virile and assertive than some colleagues, "powerful in his protestations of love", but "inclined to turn hard of tone when pushed".

He recorded the oratorio L'Enfance du Christ by Berlioz, conducted by Colin Davis, and Clairières dans le ciel, a song cycle by Lili Boulanger.