Going Evil or Good Will Effect Their Trust

To gain influence with any of the characters, you would have to agree with them when you start making decision whether it is good or evil. The influence can go up or down with the characters, so be careful.

Atton

Breakdown: Atton likes to be respected and taken seriously. He has trust issues, most of the time he would say "I trust you" will be accepted. For Dark Siders, Atton will always gain Influence when you murder the innocent. Just tell him that it was the right thing to do. Later you learn that he was trained as a Sith.

Bao-Dur

Breakdown: Gaining influence with Bao-Dur is almost entirely dependent on him being in the party to see your actions. There are no ways to increase his influence through general conversation on the Ebon Hawk.                                                             

To make Bao-Dur go to the dark side, you would need Kreia in your team, other wise you will lose influence. Also, if you ask for Kreia advice, by asking "What would you do?" and accept her judgment. Then her influence evens out.

Disciple

The Disciple only appears with a female main character, and is pretty easy to gain influence with. In fact, almost all his influence is gained through dialogue, although much of it gives light side points.             

Lowdown: You need to be supportive to the Disciple’s point of views. Which are supporting the Republic and the Jedi.