Fiber-based micro-endoscopes are a critically important tool for minimally-invasive deep-tissue imaging. However, the state-of-the-art micro-endoscopes cannot perform three-dimensional imaging through dynamically-bent fibers without the use of bulky optical elements such as lenses and scanners at the distal end, increasing the footprint and tissue-damage. Great efforts have been invested in developing approaches that avoid distal bulky optical elements. However, the fundamental barrier of dynamic optical wavefront-distortions in propagation through flexible fibers, limits current approaches to nearly-static or non-flexible fibers. Here, we present an approach that allows holographic 3D bend-insensitive, coherence-gated, micro-endoscopic imaging, using commercially available multi-core fibers (MCFs). We achieve this by adding a miniature partially-reflecting mirror to the distal fiber-tip, allowing to perform low-coherence full-field phase-shifting holography. We demonstrate widefield diffraction-limited reflection imaging of amplitude and phase targets through dynamically bent fibers at video-rates. Our approach holds potential for label-free investigations of dynamic samples