"Better Days" is your first companion mission you get from Mako as a Bounty Hunter.
As you gain affection points with your companions, they will offer you missions from time to time. Watch for the mission icon on their heads whenever you are in a Cantina. Also, they will tell you they want to talk to you in private, which often indicates a companion mission is available.
Better Days is the introductory mission to Mako. Most companions will have introduction missions which lets you know them a little better.
Every companion mission gives you a chance to get easy experience points, as well as increase your affection with the companion. Companion affection affects how fast the companions will perform crew skill tasks, as well as make more missions available to you, so you should aim to increase companion affection whenever you get the chance.
Mako: About the whole "Great Hunt" thing... Thanks. It'd mean a lot to Braden that you stuck with it.
You now are given the following dialog options on your dialog wheel:
This isn't a favor
Don't mention it.
[Flirt] What's it mean to you?
Choose the last option to flirt with Mako and get 40 affection points. Whenever you are presented with a dialog choice and have a companion with you, there is the potential that your choice will affect the companions affection. How it affects it depends on the personality of the companion.
You tell Mako you are in it for her. Mako tells you how sweet you are even though she thinks you are lieing. Great Hunt was Braden's dream. Talked about it for years. Day he told me he'd found you...should've seen him. Grinning and laughing so much she thought his face would split in half.
The next dialog wheel pops up:
I was lucky he found me
Are you sure it was Braden
Great. Can we get to work now?
Choose he first option for 15 additional affection points with Mako. It's not exactly every day you get a shot at the Great Hunt. Mako says that winning this thing would've meant more to him than revenge. So she is going to skip saying "Thank you" again, because you get the idea already. Let's just get moving.
This completes the mission "Better Days" and you get a reward of XP points as well as 55 affection points with Mako.