In this review, we study how a hybrid optomechanical system (OMS), in which a quantum micro-or nano-mechanical oscillator (MO) is coupled to the electromagnetic (EM) radiation pressure, consisting of an ensemble of ultacold atoms or an atomic Bose-Einstein condensate (BEC) can be used as an ultra precision quantum sensor for measuring very weak signals. As is well-known in any precise quantum measurement the competition between the shot noise (SN) and the backaction (BA) noise of measurement executes a limitation on the measurement precision which is the so-called standard quantum limit (SQL). In the case where the intensity of the signal is even lower than the SQL, one needs to perform an ultra precision quantum sensing to beat the SQL. For this purpose, we review three important methods for surpassing the SQL in a hybrid OMS: (i) the BA evading measurement of a quantum nondemolition (QND) variable of the system, (ii) the coherent quantum backaction noise cancellation (CQNC), and (iii) the so-called parametric sensing, the simultaneous signal amplification and added noise suppression below the SQL.