Single quotes in values should be escaped by using double single quotes in SQLite (see here). Backslashes are fine as literals. So you should use:
"INSERT INTO Artist(Id,Title) VALUES ('1','Fred''s ball \ shoe');";
The example project for cordova-sqlite-porter contains a complex example which illustrates use of both single quotes and backslashes in value strings, for example:
INSERT INTO [Artist] ([ArtistId], [Name]) VALUES (88, 'Guns N'' Roses');
INSERT INTO [Track] ([TrackId], [Name], [AlbumId], [MediaTypeId], [GenreId], [Composer], [Milliseconds], [Bytes], [UnitPrice]) VALUES (3435, 'Cavalleria Rusticana \ Act \ Intermezzo Sinfonico', 302, 2, 24, 'Pietro Mascagni', 243436, 4001276, 0.99);