In the present work we investigate effects of MeV heavy ions (from 0.4 MeV Xe to 15 MeV Si) on regularly ordered nanoparticle (NP) lattices embedded in amorphous alumina matrix. These nanostructures were produced by self-assembling growth using magnetron-sputtering deposition. From grazing incidence small-angle x-ray scattering measurements we have found that the used MeV heavy ions do not change the NP sizes, shapes or distances among them. However, ions cause a tilt of the entire NP lattice in the direction parallel to the surface. The tilt angle depends on the incident ion energy, type and the applied fluence and a nearly linear increase of the tilt angle with the ion fluence and irradiation angle was found. This way, MeV heavy ion irradiation can be used to design custom-made NP lattices. In addition, grazing incidence small-angle x-ray scattering can be effectively used as a method for the determination of material redistribution/shift caused by the ion hammering effect. For the first time, the deformation yield in amorphous alumina was determined for irradiation performed at the room temperature.