  Developing the isolation and control of ultracold atomic systems to the level
of single quanta has led to significant advances in quantum sensing, yet
demonstrating a quantum advantage in real world applications by harnessing
entanglement remains a core task. Here, we realize a many-body quantum-enhanced
sensor to detect weak displacements and electric fields using a large crystal
of $\sim 150$ trapped ions. The center of mass vibrational mode of the crystal
serves as high-Q mechanical oscillator and the collective electronic spin as
the measurement device. By entangling the oscillator and the collective spin
before the displacement is applied and by controlling the coherent dynamics via
a many-body echo we are able to utilize the delicate spin-motion entanglement
to map the displacement into a spin rotation such that we avoid quantum
back-action and cancel detrimental thermal noise. We report quantum enhanced
sensitivity to displacements of $8.8 \pm 0.4~$dB below the standard quantum
limit and a sensitivity for measuring electric fields of
$240\pm10~\mathrm{nV}\mathrm{m}^{-1}$ in $1$ second
($240~\mathrm{nV}\mathrm{m}^{-1}/\sqrt{\mathrm{Hz}}$).
