  We demonstrate successful "dry" refrigeration of quantum fluids down to
$T=0.16$\,mK by using copper nuclear demagnetization stage that is pre-cooled
by a pulse-tube-based dilution refrigerator. This type of refrigeration
delivers a flexible and simple sub-mK solution to a variety of needs including
experiments with superfluid $^3$He. Our central design principle was to
eliminate relative vibrations between the high-field magnet and the nuclear
refrigeration stage, which resulted in the minimum heat leak of $Q=4.4$\,nW
obtained in field of 35\,mT.
  For thermometry, we employed a quartz tuning fork immersed into liquid
$^3$He. We show that the fork oscillator can be considered as self-calibrating
in superfluid $^3$He at the crossover point from hydrodynamic into ballistic
quasiparticle regime.
