  CsCa$_2$Fe$_4$As$_4$F$_2$ is a newly discovered iron-based superconductor
with $T_\mathrm{c}\sim$ 30 K containing double Fe$_2$As$_2$ layers that are
separated by insulating Ca$_2$F$_2$ spacer layers. Here we report the transport
and magnetization measurements on CsCa$_2$Fe$_4$As$_4$F$_2$ single crystals
grown for the first time using the self flux of CsAs. We observed a huge
resistivity anisotropy $\rho_c(T)/\rho_{ab}(T)$, which increases with
decreasing temperature, from 750 at 300 K to 3150 at 32 K. The $\rho_c(T)$ data
exhibit a non-metallic behavior above $\sim$140 K, suggesting an incoherent
electronic state at high temperatures due to the dimension crossover. The
superconducting onset transition temperature in $\rho_{ab}$ is 0.7 K higher
than that in $\rho_c$, suggesting two-dimensional (2D) superconducting
fluctuations. The lower and upper critical fields also show an exceptional
anisotropy among iron-based superconductors. The $H_{c1}^\bot(T)$ data are well
fitted using the model with two $s$-wave-like superconducting gaps,
$\Delta_1(0)=6.75$ meV and $\Delta_2(0)=2.32$ meV. The inter-plane coherence
length $\xi_c(0)$ is $3.6$ \AA, remarkably smaller than the distance between
conducting layers (8.6 \AA), consolidating the 2D nature in the title material.
