HK-47 - Influence Increase - After completing his repairs, you'll be subjected to a brief dialog thats purpose is to facilitate adding HK-47 to your party. Immediately after it is completed, speak to him again. He will say "Statement: Master, I must say it is a pleasure to be working side by side with you.". When it is available, select "Stick with me - you'll pick up a few things." for an influence boost.
Hanharr - Influence Increase - Go speak to Hanharr. He will comment on your Dark Side visage and eventually you'll be able to interject with some questions. Mention that you've heard that he hunts humans and when he says "No human must survive, those that do must be taught what life debts are - and why they will pay the price for my people.", reply with either "But still you serve me, as a slave should. You know your place." or "Any human that cannot stand against you deserves to die.". Nothing more can be gained from speaking to him at this time, so cut the conversation short and find Kreia.
Kreia - Influence Increase - You will need to speak to Kreia to trigger the Lesson of Strength, however if you have 14 Wisdom or higher, you can save some time and complete the lesson now. If you are able to do so, you will gain some significant goodies along with some Dark Side points, an influence gain with Kreia, and 500 XP. If you don't, not to worry, you can still complete the lesson later, but you will need to boost your Wisdom first.
NOTE: You now have sufficient influence over Kreia to ask her about Revan and unlock the last of her little secrets.
G0-T0 - Influence Increase - Speak to G0-T0 and question him about saving the Republic. Mention that you might be willing to help out for some credits. When he states "For every system you stabilize, I will reward you for your efforts.", reply with "If you have the credits, then that is all I needed to hear.", "I will do what has to be done, no matter what the cost.", or "If I have to kill everyone to do it, you'll get your stability."
NOTE: Head to the Galaxy Map and set course for Dxun.
HK-47 - Influence Increase/Hanharr - Influence Increase - After your meeting with Mandalore, make your way back out into the jungle. Seek out Kumus and use the permacrete detonator to blow him up. Due to a rather fortutitious oversight, this act will gain you double the usual influence with HK-47.
Hanharr - Influence Increase - Take a moment to speak to Hanharr. Ask him about his shackles. Keep the conversation going, making sure to ask about Czerka and his people. When he states "Metal they placed upon my wrists and neck, to keep me bound and weak. They were not strong enough to hold me otherwise.", reply with either "Yet somehow, they were strong enough to cage you - as it should be." or "Perhaps you are weak in that you allowed the shackles to be placed at all."
Eventually he will tell you about how he came to be on Nar Shaddaa. When the opportunity is available, comment that "You can't have been the only slave Czerka took from your world.". Settle in and prepare for a long story about Czerka and the Wookies. After some time, you will have an opportunity to comment on Hanharr's acts. He will say "But there is one truth that you know - that all life is connected, and there is life and light after the black of the Shadowlands.". Reply with either "You lessen an act of slaughter by thinking it was salvation." or "The only truth is that you killed your tribe because they were weak - which is what they deserved."
But wait, there's more. He will mention that he wants to leave the Shadowlands and bemoan "Yet I am trapped here with you, in this cage, surrounded by the stench of human animals.". Comment that "What you did to your people was madness - yet there was strength in it." and he will begin speaking of Malachor V. When he says "I know that you did no such thing with your own tribe. They died alone, in pain, and the only one to hear them die was you.", reply with either "If you think such deaths bother me, they do not." or "Everyone at Malachor died because they had to - and I would destroy them all again, gladly." A few exchanges more and the conversation will be finished.
Speak to Hanharr one more time and tell him that you wish to share your lesson of strength with him. Just keep him talking and eventually he will break beneath your will, unlocking the last of your rewards and finalizing your influence over him.
HK-47 - Influence Increase - Speak to HK-47 again and ask him about his previous master. He will offer a rather humorous commentary on some of the party members from the first game. When you attempt to exit the conversation, he will interrupt with a question. Respond with "The next person who prevents me from leaving when I say the conversation is over is going to die. Now let me go, or else." for another influence increase.
Talk to him again, asking him about his earlier inquiry about the Mandalorian Wars. Follow this vein until the conversation turns toward Revan and his/her conversion of the Jedi. Select "I can't allow you to remain on this ship if you've killed Jedi." then respond to his answer with either "If you say that again, I will destroy you." or "If I had known what would happen, I might have done it intentionally."
NOTE: Finish your business on Dxun and head to Onderon. If you haven't already, be sure to spend any Force Powers that you earn at level ups to pick up Affect Mind.