The optofluidic microscope (OFM) is a lensless, low-cost and highly compact on-chip device that can enable high-resolution microscopy imaging. The OFM performs imaging by flowing/scanning the target objects across a slanted hole array; by measuring the time-varying light transmission changes through the holes, we can then render images of the target objects at a resolution that is comparable to the holes' size. This paper reports the adaptation of the OFM for imaging Giardia lamblia trophozoites and cysts, a disease-causing parasite species that is commonly found in poor-quality water sources. We also describe our study of the impact of pressure-based flow and DC electrokinetic-based flow in controlling the flow motion of Giardia cysts--rotation-free translation of the parasite is important for good OFM image acquisition. Finally, we report the successful microscopy imaging of both Giardia trophozoites and cysts with an OFM that has a focal plane resolution of 0.8 microns.