The following paper introduces Dual beam-similarity awaRe Integrated sensing and communications (ISAC) with controlled Peak-to-average power ratio (DRIP) waveforms. DRIP is a novel family of space-time ISAC waveforms designed for dynamic peak-to-average power ratio (PAPR) adjustment. The proposed DRIP waveforms are designed to conform to specified PAPR levels while exhibiting beampattern properties, effectively targeting multiple desired directions and suppressing interference for multi-target sensing applications, while closely resembling radar chirps. For communication purposes, the proposed DRIP waveforms aim to minimize multi-user interference across various constellations. Addressing the non-convexity of the optimization framework required for generating DRIP waveforms, we introduce a block cyclic coordinate descent algorithm. This iterative approach ensures convergence to an optimal ISAC waveform solution. Simulation results validate the DRIP waveforms' superior performance, versatility, and favorable ISAC trade-offs, highlighting their potential in advanced multi-target sensing and communication systems.