This group of achievements correspond with the new date events added for the four romancable companions added with Knights of the Fallen Empire and Eternal Throne. There are 220 legacy points spread between 12 achievements in 4 subsections. There are a total of 6 legacy titles, 1 Advisor's Dejarik Table, 1 Jorgan's Rifle Case, 1 Makeb Museum Display, 1 Mounted Training Sabers, 1 Salted Marsh Grub Platter, and 1 Theron's Broken Datapad. These achievements can either be very easy to complete, if you already romanced all the required companions, or incredibly dull and grindy if you didn't romance any of the companions on your characters.
This brief guide is for anyone who has not already committed to the four romances on their characters. Also note that these are my personal findings from completing the achievements on my own account, if you have a better method of leveling or aren't cheap like me then do whatever works best for you.
Character Creation: I created Republic faction characters that could stealth for all of these achievements. My reasoning for faction was that autocompleting the story on a Republic character means the game automatically selects light side choices which is useful for locking in Arcann's romance. While not strictly necessary I wanted to be as safe as possible. Stealthers were chosen just to get through the slog of enemies in the Fallen Empire and Eternal Throne chapters since I had to make three new characters for these achievements.
Leveling Characters: I was lucky enough to start leveling my characters during the double experience event, which made the whole process of leveling characters way less painful than it otherwise would have been. I unlocked the class story and exploration experience buffs in the character legacy window, and made sure to have an experience buff active all the time. After hitting level 50 I travelled to Makeb and used the GSI Satellite Support Terminal to get the GSI Satellite Support buff. One of the passives from this buff is a 150% bonus to exploration experience, and usually resulted in ~5 additional levels just from exploring all the map sections of Makeb. I then ran heroics until I reached level 65 and was able to skip the story to the beginning of Knights of the Fallen Empire.
Note: If you aren't worried about spending credits or cartel coins you can buy a Commander's Character Token or Master's Datacron to reach the required level to skip ahead in the story to Knights of the Fallen Empire
I completed the Knights of the Fallen Empire story up to Chapter IX: The Alliance, and selected one companion to romance for each of my three characters.
Note: You cannot reset a companion's romance by restarting Chapter IX, hence the need to create three characters if you have already completed the story on a character or selected someone else to romance.
I completed the 5 time weekly mission on each character to unlock the final achievement for Lana, Theron, and Koth. For Arcann, since his romance is locked in later in the story I was then able to take one of the characters and skip ahead in the story to the start of Knights of the Eternal Throne. I then played through all the chapters until Chapter VI: The Dragon's Maw to ensure that I recruited Arcann as a companion.
Note: This may happen automatically when you skip ahead in the story as a light side character, but I wasn't willing to test this theory on a character I had made specifically to get the romance achievements.
After I had Arcann as a companion I skipped ahead in the story to the Ossus mission, Inflection Point, to unlock Arcann's companion alert, Unmasked Regret, where you are able to confirm Arcann's romance and overwrite any other companion's romance. This allowed me to complete the four romances with only three characters.
10 Legacy Points | 20 Legacy Points | 25 Legacy Points
Grants Legacy Titles: Arcann's Admirer on completion | Grants Mounted Training Sabers on completion
These achievements are unlocked for completing Arcann's date night once, three, and five times. The mission needed to complete these is;
[Date Night] Dueling Hearts
10 Legacy Points | 20 Legacy Points | 25 Legacy Points
Grants Legacy Titles: Koth's Kindred on completion | Grants Salted Marsh Grub Platter on completion
These achievements are unlocked for completing Koth's date night once, three, and five times. The mission needed to complete these is;
[Date Night] A Place to Call Home
10 Legacy Points | 20 Legacy Points | 25 Legacy Points
Grants Legacy Titles: Lana's Lover on completion | Grants Advisor's Dejarik Table on completion
These achievements are unlocked for completing Lana's date night once, three, and five times. The mission needed to complete these is;
[Date Night] Dejarik for Two
10 Legacy Points | 20 Legacy Points | 25 Legacy Points
Grants Legacy Titles: Theron's Treasure on completion | Grants Theron's Broken Datapad on completion
These achievements are unlocked for completing Theron's date night once, three, and five times. The mission needed to complete these is;
[Date Night] You Work too Hard
10 Legacy Points | 20 Legacy Points | 25 Legacy Points
Grants Legacy Titles: Jorgan's Joy on completion | Grants Jorgan's Rifle Case on completion
These achievements are unlocked for completing Aric's date night once, three, and five times. The mission needed to complete these is;
[Date Night] Target Practice
10 Legacy Points | 20 Legacy Points | 25 Legacy Points
Grants Legacy Titles: Vette's Vow on completion | Grants Makeb Museum Display on completion
These achievements are unlocked for completing Vette's date night once, three, and five times. The mission needed to complete these is;
[Date Night] Vette at the Museum