  Squeezing is a crucial resource for quantum information processing and
quantum sensing. In levitated nanomechanics, squeezed states of motion can be
generated via temporal control of the trapping frequency of a massive particle.
However, the amount of achievable squeezing typically suffers from detrimental
environmental effects. We analyze the performance of a scheme that, by
embedding careful time-control of trapping potentials and fully accounting for
the most relevant sources of noise -- including measurement backaction --
achieves significant levels of mechanical squeezing. The feasibility of our
proposal, which is close to experimental state-of-the-art, makes it a valuable
tool for quantum state engineering.
