We introduce the Serendipitous H-ATLAS-fields Observations of Radio Extragalactic Sources (SHORES) multiple pencil beam survey that observed at 2.1GHz with the Australia Telescope Compact Array (ATCA) 29 fields in total intensity and polarization within the Herschel-ATLAS Southern Galactic Field. This paper presents the observations, calibration and analysis of the 27 shallow fields that cover an overall area of ~26 square degree with increasing sensitivity towards the phase centers of each pointing according to the ATCA 22 m dish response function, down to {sigma}<~33uJy. Two additional (deep) fields have been observed to even higher sensitivity. All the SHORES observations have been calibrated to account also for linear polarization. Polarization and deeper field analysis will be presented in future papers. The SHORES shallow-field sample considered in the present paper counts 2294 sources detected with BLOBCAT to signal-to-noise ratio SNR>~4.5. Simulations determined that our procedure and final catalog is 95% reliable above 497.5uJy and 95% complete to the SNR>~4.5 significance level. By exploiting ATCA E-W 6km configuration we reached resolutions of 3.2"x7.2", to which level 81% of our sources are unresolved. We determined source counts down to the 150uJy level. For the sources with a counterpart in H-ATLAS, the FIR-radio correlation is calculated and discussed.