In this work, we synthesized a series of peptoid-based histone deacetylase (HDAC) inhibitors with variations in the linker region and zinc-binding groups. All compounds were investigated for their HDAC inhibition, antiplasmodial activity, and cytotoxicity against native and cisplatin-resistant carcinoma cell lines. The ethylhydrazide 20 (DS-103) proved to be the most effective compound in these primary screenings. DS-103 showed nanomolar inhibition of class I HDACs and of HDAC6 (class IIb). To further investigate the binding mode of DS-103, a crystal structure of DS-103 in complex with HDAC6 was obtained, which represents the first reported crystal structure of an alkylhydrazide in complex with an HDAC enzyme. Importantly, DS-103 completely reversed cisplatin resistance in two different platinum-resistant solid cancer cell lines and demonstrated strong synergism with cisplatin. The synergistic anticancer effects are mediated by increased DNA damage and p21 expression, resulting in caspase-mediated apoptosis and cell death.