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Protección (DFPS) a consecuencia de una audiencia adversa. .... (DFPS) following an adversary hearing under Section 262.201, Family Code (attach ...

This phrase means 'trial'; a proceeding involving a real controversy contested by two opposing PARTIES, before an impartial judge.

A civil lawsuit hearing in which a final judgment is made may also be a 'trial'. Rather than the query wording, the usual term is an 'adversary proceeding'. Both parties have the right to be present before the court and a final decision may be made in the case.
It is in contrast or opposite in meaning with proceedings such as 'ex-parte hearings / ex-parte written motions' and 'friendly suits/lawsuits' in which only one party appears or acts before the court, because either there is no controversey between the parties (uncontested divorce, etc.) or because one party has the right to take some step without opposition.
(Source: Barron's Legal Dictionary, Steven H. Gifis (1996)

The 'full' part of the query is just legaleze wording. My suggested translation into Spanish localized legaleze may be improved by native Spanish colleagues.
Hope this helps. Regards.

Espero te sirva!

El mediador tratara de ayudarlos resolver sus conflictos sin el costo y tiempo que se tarda una audiencia completa con el juez. No nesecita abogado para ...
www.lanwt.org/txaccess/spanish/lf.asp

Si el juez le da la orden de protección preliminar, durará 15 días o hasta la audiencia. completa. La audiencia completa es cuando usted y la otra persona ...
www.icandocs.org/va/test

Una comunicación pro-activa sobre una audiencia completa de “stakeholders”, para asegurar la. imagen, la sostenibilidad y el desarrollo de la empresa ...
www.augure.com/ES/imgpages/communiques/Augure.pdf