Step 1: Understanding the Concept:
The hybridisation of a complex depends on the metal electron configuration and the strength of the ligand field.
Step 2: Find the Oxidation State:
In \([\text{NiCl}_4]^{2-}\), \(x - 4 = -2\), so Ni is \(+2\) and has the configuration \(3d^8\).
Step 3: Ligand Field:
Chloride is a weak field ligand. It does not force the d electrons to pair, so the 3d orbitals stay occupied and the 4s and 4p orbitals are used.
Step 4: Hybridisation:
One 4s and three 4p orbitals mix to give four \(sp^3\) orbitals, so the shape is tetrahedral and the complex is paramagnetic with two unpaired electrons.
A \(dsp^2\) square planar shape would need strong field ligands such as \(\text{CN}^-\). The \(sp^3d^2\) and \(d^2sp^3\) types give six-coordinate octahedral shapes, which need six ligands.
Final Answer:
The complex is tetrahedral with \(sp^3\) hybridisation, option (A).
\[ \boxed{\text{(A) } sp^3} \]