Soft robotic manipulators are generally slow despite their great adaptability, resilience, and compliance. This limitation also extends to current soft robotic micromanipulators. Here, we introduce FilMBot, a 3-DOF film-based, electromagnetically actuated, soft kinematic robotic micromanipulator achieving speeds up to 2117 $\deg$/s and 2456 $\deg$/s in $\alpha$ and $\beta$ angular motions, with corresponding linear velocities of 1.61 m/s and 1.92 m/s using a 4-cm needle end-effector, and 1.57 m/s along the Z axis. The robot can reach ~1.50 m/s in path-following tasks, operates at frequencies up to 30 Hz, and remains functional up to 50 Hz. It demonstrates high precision (~6.3 $\mu$m, or ~0.05% of its workspace) in small path-following tasks. The novel combination of the low-stiffness soft kinematic film structure and strong electromagnetic actuation in FilMBot opens new avenues for soft robotics. Furthermore, its simple construction and inexpensive, readily accessible components could broaden the application of micromanipulators beyond current academic and professional users.