App 1 to JAR-FCL 1.160 is quite clear:
(c) 20 hours of cross-country flight as pilot-in-command including a VFR cross-country flight totalling at least 540 km (300 NM) in the course of which full stop landings at two different aerodromes from the aerodrome of departure shall be made;
So it must be VFR
You must be PIC
It must be 540Km (300nm) Actually 293nm
You must land at two other places other than the point of departure.
The within "1 day" is an interpretation, as the requirement refers to a flight (singular) this effectively requires each leg to follow the previous leg and not be spread over a number of days days.
It is not a Qualifying X Cty such as the PPL, you don't have to be solo and you don't need signatures or a certificate, just log book evidence of meeting the requirement. Cabair aircraft are regularly seen going around in a loose formation!