ISOLTRAP, located at the radioactive-ion beam facility ISOLDE at CERN, provides high-precision mass values of short-lived nuclides as well as precision β-decay Q-values for nuclear models and fundamental interactions. Previously, the measurements were made using the time-of-flight ion-cyclotron-resonance (ToF-ICR) detection technique, which is limited in accessible half-live, resolving power and relative uncertainty. More recently, the new phase-imaging ion-cyclotron-resonance (PI-ICR) detection technique [S. Eliseev et al., Phys. Rev. Lett. 110 082501 (2013)] enables complementary experiments, with fewer ions and increased resolving power, providing access to new areas of the nuclear chart and to new physics. This contribution will report on the implementation and further development of PI-ICR mass spectrometry (MS) with ISOLTRAP, including results from first on-line measurements in both the high-resolution and high-precision regimes. In particular, the Q-value of the 88Sr-88Rb β-decay was determined with an uncertainty of < 130 eV. Furthermore, the separation of the low-lying isomeric states in 127Cd and 129Cd was achieved, from which their excitation energies were determined. A mass resolving power m/Δm > 106 was reached for only 100 ms measurement time compared to m/Δm ~ 104 – 105 using ToF-ICR MS.