This page of our guide to Greedfall features the walkthrough of the side quest, The Trial.
Where to start the quest?: Complete The Experiments of Dr. Asili side quest.
Contact the lawyer, talk about the case and you will get a lot of quests. Talk to Aphra about Asili - you can ask the woman when she is in your party, or, for example, in the mansion. Then go to Nauts and convince them to testify (you will do this by repelling the attack of their enemies).
Go back to Asili's lab and find evidence in his quarters. In a chest in his office, you will also find a legendary gun. Now go to the survivors in Vigshadir and convince them to testify against the mad doctor.
Ask the researchers at Hikmet's lab to testify (they'll be happy to if you let them go). Finally, convince Dr. Onur to testify against Asili. You can achieve this by using intuition on level 3 or through Aphra's intervention.
Run to the attorney and examine a sample of black powder with the help of the doctor's assistants. Once again return to the attorney, submit all the evidence and start the trial. Whew! After the cutscene, you will get + 3 reputation with Bridge Alliance. For superb work and ethics in the quest, you will get another +5 reputation with Alliance Bridge. Now add Aphra to your party and go with her to the execution place of the doctor. After the cutscenes, you will get 2200 XP and complete the task.