Step 1: Understand the term "Anamniotic tetrapod".
\begin{itemize}
\item Tetrapod: An animal with four limbs (or descended from an ancestor with four limbs). This group includes amphibians, reptiles, birds, and mammals.
\item Anamniotic: Refers to vertebrates whose embryos develop without an amnion (a protective membrane surrounding the embryo). Anamniotic vertebrates typically lay their eggs in water or moist environments, and the larvae develop in water. This characteristic is found in fish and amphibians.
\end{itemize}
Combining these, an "anamniotic tetrapod" refers to a tetrapod that lacks an amnion during embryonic development, which specifically points to Amphibians. Reptiles, birds, and mammals are amniotes (they develop an amnion).
Step 2: Evaluate each option based on the definition.
\begin{itemize}
\item (1) Pristis: This is a genus of sawfishes, which are cartilaginous fish (Chondrichthyes). Fish are anamniotic, but they are \textit{not} tetrapods (they have fins, not limbs). So, Pristis is an anamniotic non-tetrapod.
\item This option is incorrect.
\item (2) Hyla: This is a genus of tree frogs, which are Amphibians. Amphibians are tetrapods and are characterized by their anamniotic development (eggs laid in water, larval stage in water without an amnion).
\item This option is correct.
\item (3) Sphenodon: This is a genus of tuataras, which are Reptiles. Reptiles are tetrapods but are amniotes (their embryos develop within an amnion, allowing them to lay eggs on land).
\item This option is incorrect.
\item (4) Psittacula: This is a genus of parakeets, which are Birds. Birds are tetrapods and are amniotes (their embryos develop within an amnion in a shelled egg laid on land).
\item This option is incorrect.
\end{itemize}
Step 3: Conclude the correct option.
Based on the definitions, \textit{Hyla} (tree frog) is the only anamniotic tetrapod among the choices.
The final answer is $\boxed{\text{Hyla}}$.