Atton Increase - Be nice with him, but not too nice, otherwise you get LS points
Kreia - Influence Decrease - "Watch that tone, old woman - I will not be lectured by you" after she reminds you that "Our enemies gather while we wait here."
NOTE: Once you make it onto the Engine Deck, Atton will interrupt with a premonition. There are some influence laden responses here, however you goal is to avoid either gaining or losing influence at this point. You can accomplish this by responding to his comments with "What's wrong?" followed by "Save your feelings for when we're out of here.".
T3-M4 - Influence Decrease - "We may still have a use for you. Follow me." while he's telling you about being ambushed by the HK-50 unit.
Ebon Hawk - Escape From Peragus
Kreia - Influence Increase - "If your training brings me power, then I will listen." after she offers to help you reestablish your connection to the Force.
Atton - Influence Increase/Kreia - Influence Decrease - After making an impression on the local law enforcement, head out into Residential Module 082 East (Apartments). Head across the hall to the cluster of apartments opposite those you just left. In the center apartment is a footlocker that you can ransack. After doing so, you will be approached by the apartment's righful resident. Pick a fight and kill him to gain influence with Atton and lose influence with Kreia.
Atton - Influence Increase - While running errands for Luxa, you'll be asked to collect a debt from Opo Chano. Remove Kreia from your party before speaking with Opo, then take a hard line with him and kill him when you get the chance. Another influence increase with Atton.
After that, you'll finally get your chance to meet with Lopak Slusk. While on your way to the meeting, kill the receptionist for yet another influence bump. Feel free to leave the module and add Kreia back to your party before you proceed to your confrontation with Lopak Slusk.
Bao-Dur - Influence Decrease - Inside the Underground Base, you will encounter a Czerka employee that's been trapped there. Follow the Dark Side options until you have a chance to kill him and get your first influence decrease with Bao-Dur.
Bao-Dur - Influence Decrease - Seek out your party members after arriving in the Secret Academy. After Bao-Dur wakes up and says "I... am sorry, General. I must have lost consciousness in the crash." reply with either "We could have used you earlier when we were ambushed. Do not fail me again." or "I have no use for a soldier who falls at the first sign of combat. Be on your guard in the future.". Follow this up with "This'll be your new home if your wounds could slow me down. Understand?" and "Just go to the ship - I will deal with your failure later." when available.
T3-M4 - Influence Decrease - After recovering T3-M4 in the Hidden Academy, select "Don't waste my time with excuses." while discussing his capture.
Ebon Hawk - Escape From Telos
NOTE: Many of the INF opportunities in this section are related to Handmaiden. If your PC is female, then Handmaiden will not appear during this exchange and the INF options listed here will not apply. Female PCs will instead meet up with Disciple on Dantooine. From this point forward, entries for Handmaiden and Disciple may be found side-by-side.
Handmaiden - Influence Increase - Interestingly, your objective during your very first influential meeting with Handmaiden is to avoid influence-related options altogether. Unfortunately, this isn't possible, but you can minimize the damage. During the cutscene select "Do you think we need help?" followed by "When you put it like that, then welcome aboard.". While this isn't exactly Dark Side, it is important to note that the Dark Side options would have cost you influence that would be impossible to regain without gaining Light Side points. For the final part of this conversation, select either "Look, forget Atton. Take the regular quarters, we have enough room." or "Don't let them bother you - we've just been through a lot."
After the cutscene, the gloves come off so go speak to Handmaiden and initiate the first of three duels with her. If you win, you will gain influence with her.
With that accomplished go back and select "I wanted to ask you about Atris.". Stick with first option until you get to the part where she states "I see. I have asked you many questions - I did not mean to. They are questions that have gathered over years, and I did not wish to ask Atris.". Reply with "Only fools fear questions - and their answers."
NOTE: It is important that you ask her about Atris before getting to 69% influence or higher. Apparently, once Handmaiden starts taking a liking to you, the subject of Atris makes her moody.
Speak to her one more time and ask her "Why do you look different than your sisters?". You will have sufficient influcence to unlock convince her to share her family history. The objective here is to make it to the end of the conversation where she swears alligience to you. If you make it there, you will gain another dose of influence.
NOTE: After you've finished speaking to Handmaiden, seek out Kreia. She seems upset that others are joining you. Stick with Dark Side options and end this conversation as soon as it runs it course. Now talk to her again and she will begin to question the amount of time that you are spending with Handmaiden. Stick to Neutral/Dark Side options here and finish the conversation. She will mention Handmaiden's Jedi heritage, unlocking a vital dialog option that will allow you to gain influence with Handmaiden later in the game. You can go speak to Handmaiden again, however you will not have sufficient influence with her to complete that portion of the dialog.
Kreia - Influence Increase - Talk to Kreia again. She will mention that you are getting more powerful and then caution you about falling to the Dark Side. You will eventually come to a point in the conversation where you have to comment on your regard for your party members. Select "Then I shall view you as disposable, then."
After this, let Kreia know that you have more questions and then ask her why she doesn't like Handmaiden. Again, just stick with Dark Side options, specifically either "Agreed. We need every tool we can get if Atris tries anything." or "I will keep in that mind - and watch the Handmaiden carefully." after she says "Do not see every enemy as an enemy - see them instead as an ally, whether they realize it or not. This situation may yet work to our advantage."
T3-M4 - Influence Decrease - Find T3-M4 and ask him, "How's the Ebon Hawk". Reply to answer with either "Just be sure it stays that way, or we'll be using you for spare parts." or "Keep up the routine maintenance. If something goes wrong, I'll hold you responsible." Now ask T3-M4 to show the list of Jedi Masters again. When he's finished tell him, "If you do that again, I'll have you memory wiped. Understand?"
Last one. This influence opportunity will only be available if your Intelligence is at least 14 and your Computer Usage Skill is at least 10. Use whatever boosting items and Force powers you have, and then go speak to T3-M4 one last time. You should now see, "[Intelligence] How did you get here, T3?" in your list of dialog options. Follow this up with "[Computer] That does it. I'm going to rip out your module and get some answers." and then "I don't care what damage it could cause - I want to know what you're hiding.". This will unlock a hidden message that he is storing. Depending on Revan's gender and alignment, you'll find a message from either Bastila or Carth.
There are more Dark Side influence opportunities after the message is finished playing however, you've already bottomed-out your influence with T3-M4, so you can opt to end the conversation now. If you haven't already, make sure that you've beefed up your Computer Usage and Repair skills and get to work on T3-M4 for some really cool upgrades and XP.
NOTE: There are no additional influence opportunities at this time. Go the Galaxy Map and head for Nar Shaddaa.