Like the other Romance quests, there are 3 of them and you can activate them by talking to Siora at any time with Y. After each quest, you also talk to Siora to see how she feels afterward. The answer you pick can increase or decrease your rep with her so here are the answers to pick after each:
After "Find Queen Bladnid":
Obviously for "Promises Set in Stone", do NOT accept
BTW, this quest doesn't appear until after
so don't worry if it hasn't popped up yet.
After "Promises Set in Stone":
Lastly, after "The Queen's Farewell":
I had to wait a day or two after completing the previous quest in order for this one to show up so just go sleep at the fire for a day and she should get the Exclamation marked speech bubble after that indicating she's ready to give you a quest.
Then speak to her one more time to accept the Rendezvous, meet her in your bedroom, and tell her you love her after the scene in your bedroom then Boom! Achievement.