Taken from the Crown Prosecution Service guidance[0], which isn't gospel, but is usually a pretty accurate reflection of the law, the grounds the court must consider are:

- the conduct described in the warrant amounts to an extradition offence;

- any of the statutory bars to extradition apply;

- there is prima facie evidence of guilt (if applicable, see below);

- extradition would be disproportionate or would be incompatible with the requested person’s human rights.

The statutory bars to extradition, taken from the same document include whether the subject would face the death penalty.

It's not clear to me from this article which of the points of law above is being argued. Some of the testimony appears (or at least the reporting of it) appears to include an element of trying to demonstrate that the extradition is politically motivated. It probably is, but they'll have to establish one of the above specific points.

Note that I'm not claiming that the above points can't be established here - I'm just not seeing the direct link from the reporting on the case, in this article and others, to how they're attacking the legal aspect.

[0] https://www.cps.gov.uk/legal-guidance/extradition