Data returned from the Cassini-Huygens mission have strengthened Enceladus, a small icy moon of Saturn, as an important target in the search for life in our solar system. Information gathered from Cassini to support this includes the presence of a subsurface liquid water ocean, vapor plumes and ice grains emanating from its south polar region, and the detection of essential elements and organic material that could potentially support life. However, several outstanding questions remain regarding the connectivity of plume material to the ocean and the composition of the complex organic material. Herein we introduce Tiger, a mission concept developed during the 2020 Planetary Science Summer School at NASA's Jet Propulsion Laboratory. Tiger is a flyby mission that would help further constrain the habitability of Enceladus through two science objectives: (1) determine whether Enceladus's volatile inventory undergoes synthesis of complex organic species that are evidence for a habitable ocean, and (2) determine whether Enceladus's plume material is supplied directly from the ocean or if it interfaces with other reservoirs within the ice shell. To address the science goals in a total of eight flybys, Tiger would carry a four-instrument payload, including a mass spectrometer, a single-band ice-penetrating radar, an ultraviolet imaging spectrograph, and an imaging camera. We discuss Tiger's instrument and mission architecture, as well as the trades and challenges associated with a habitability-focused New Frontiers-class flyby mission to Enceladus.