3 down: Pet mules seen on beach (6, 9)
Classic: pet mules = budgie smugglers = seen on beach.
19 down: Southern nation I left quietly in drag (7)
The more Yiddish the better I say: Southern nation I left quietly = s Chile – i pp = schlepp = drag.
20 down: Professional hits upbeat times? Not first of all (7)
Exceptionally well-hidden direct clue: upbeat times not first of all = up drum eras not a = murd eras – a = murders = professional hits.
11 across: A case of ‘That’s it, Ernesto!?’ (7)
How much of Che Guevara’s fame can be put down to his name’s use in cryptics? Great clue: that’s it, Ernesto! = atta (think ‘atta boy’) Che = attache = a case.
22 down: Mercury in rock shelf finally prepared in report (7)
A fundamentally fair clue that is so cleverly constructed that it’s rather difficult to decipher: shelf finally prepared in report = f ready in report = Freddie = Mercury in rock.