Transition metal coordination compounds play an important role in the treatment of neoplastic diseases. However, due to their low selectivity and bioavailability, as well as the frequently occurring phenomenon of drug resistance, new chemical compounds that could overcome these phenomena are still being sought. The solution seems to be the synthesis of new metal complexes conjugated with drug carriers, e.g., dendrimers. Numerous literature data have shown that dendrimers improve the bioavailability of the obtained metal complexes, solving the problem of their poor solubility and stability in an aqueous environment and also breaking down inborn and acquired drug resistance. Therefore, the aim of this study was to synthesize a novel imidazole platinum(II) complex conjugated with and without the second-generation PAMAM dendrimer (PtMet2–PAMAM and PtMet2, respectively) and to evaluate its antitumor activity. Cell viability studies indicated that PtMet2–PAMAM exhibited higher cytotoxic activity than PtMet2 in MCF-7 and MDA-MB-231 breast cancer cells at relatively low concentrations. Moreover, our results indicated that PtMet2–PAMAM exerted antiproliferative effects in a zebrafish embryo model. Treatment with PtMet2–PAMAM substantially increased apoptosis in a dose-dependent manner via caspase-9 (intrinsic pathway) and caspase-8 (extrinsic pathway) activation along with pro-apoptotic protein expression modulation. Additionally, we showed that apoptosis can be induced by activating POX, which induces ROS production. Furthermore, our results also clearly showed that the tested compounds trigger autophagy through p38 pathway activation and increase Beclin-1, LC3, AMPK, and mTOR inhibition. The high pro-apoptotic activity and the ability to activate autophagy by the imidazole platinum(II) complex conjugated with a dendrimer may be due to its demonstrated ability to reverse multidrug resistance (MDR) and thereby increase cellular accumulation in breast cancer cells.