Context. We investigate the physico-chemical properties of the planetary nebula (PN) NGC 3242 in both 1D and 2D, using integral field unit (IFU) data. This PN has a complex morphology with multiple shells and contains a pair of structures with a lower degree of ionization compared to the main nebular components. The origin of these so-called low-ionization structures (LISs) remains a mystery. Aims. With the capabilities offered by IFU spectroscopy, we aim to gain a better understanding of the behavior of nebular properties in the LISs and examine the spatial distribution of physico-chemical parameters in NGC 3242. Methods. Data from the Multi Unit Spectroscopic Explorer (MUSE) at the Very Large Telescope (VLT) were used in order to perform a spatially resolved physico-chemical analysis of NGC 3242. The analysis was performed both in 2D, based on emission line maps, as well as in 1D, via simulations of long-slit spectroscopy, with pseudo-slits. Results. Through the deeper investigation of MUSE data, we detected new structures perpendicular to the pair of LISs of NGC 3242, which are mainly seen in the light of [S III] and [N II]. In addition, two arc-like structures were revealed. Moreover, an inner jet-like structure was found through its [Fe III] emission. The interaction of the jet with the rim may be related to the formation of knots and blobs. The higher value of Te, is estimated from the [S III] diagnostic lines, followed by Te [N II]), Te (H I) and, finally, Te (He I). In all cases, Te is higher at the inner nebular structures. Regarding electron density, ne, is lower at the LISs, while an increase is observed at the nebular rim. Diagnostic diagrams confirm that NGC 3242 is a highly ionized nebula. Moreover, for the first time, the MUSE data have unveiled the atomic line [C I] λ8727 in this PN, which is primarily emitted from the LISs. This finding suggests that these structures may consist of a molecular core surrounded by neutral and ionized gas.