The phrase "attempting to challenge that" is correct and usable in written English.
You can use it when discussing efforts to question or dispute a particular idea, statement, or situation.
Example: "The researchers are attempting to challenge that widely accepted theory with new evidence."
Alternatives: "trying to contest that" or "seeking to dispute that".
In its early attempts to challenge that perception, Nord-Pas-de-Calais branded itself as France's "museum region".
The HomePod, on the other hand, is an attempt to challenge that idea — and the idea that a smart speaker can't be a useful product, divorced of its assistant.
If you are attempting to challenge yourself, that is okay.
Attempting to challenge assumptions that people in the south support a party for different reasons than those in northern areas, Denham will put polling carried out by YouGov/Demos showing "little overall difference in overall attitudes between regions" at the centre of his argument that Labour can win support in southern England.
Mumsnet is attempting to challenge what it calls "persistent myths that help to make society less sympathetic" and stop victims reporting attacks.
It attempts to challenge the claim that an external standard of morality prevents God from being sovereign by making him the source of morality and his character the moral law.
Ostensible worker representation is provided by the Workers Housee, a state-sponsored institution that attempts to challenge some state policies.
The message also attempted to challenge Obama's insistence that the group was not Islamic and that its actions, particularly the killing of innocents, were not condoned by any religion.
This study will attempt to challenge the traditional assumption that formalization hinders innovation.
I'm already on record as a critic of the American warrantless wiretapping programs, since I filed an amicus brief in Clapper v. Amnesty International, the case before the US Supreme Court this term that attempted to challenge the program.
