We report on a family of complex birefringent elements, called Multi-Twist Retarders (MTRs), which offer remarkably effective control of broadband polarization transformation. MTRs consist of two or more twisted liquid crystal (LC) layers on a single substrate and with a single alignment layer. Importantly, subsequent LC layers are aligned directly by prior layers, allowing simple fabrication, achieving automatic layer registration, and resulting in a monolithic film with a continuously varying optic axis. In this work, we employ a numerical design method and focus on achromatic quarter- and half-wave MTRs. In just two or three layers, these have bandwidths and general behavior that matches or exceeds all traditional approaches using multiple homogenous retarders. We validate the concept by fabricating several quarter-wave retarders using a commercial polymerizeable LC, and show excellent achromaticity across bandwidths of 450-650 nm and 400-800 nm. Due to their simple fabrication and many degrees of freedom, MTRs are especially well suited for patterned achromatic retarders, and can easily achieve large bandwidth and/or low-variation of retardation within visible through infrared wavelengths.