Shyka the Many can be met in a variety of occasions through the course of the game. They might show up just for a little chit chat, in form of flashbacks, or play an active role in specific quests, either side or main story related. As I am unsure about which 'meetings' count towards the completion of the achievement, I will list all the times I personally met them (which are more than the three times required but granted me the achievement nevertheless):
• Shyka can be met during both Jubilost's companion sidequests: “The Price of Curiosity” at the Inconsequent Debates in Chapter 3, and “Door to Nowhere” at the Cave from Luna's Map around Chapter 5. In both occasions, their name will be The Host instead of Shika the Many. Additional infos about Jubilost and his personal quests can be found in the Companions section.
• Can be briefly met in Lostlarn Keep during the Varnhold's Lot DLC but, being DLC related, there is a high chance this one might not be required.
• During War of the River Kings in Chapter 6, the Storyteller will let you know about a way to possibly peek into Nyrissa's past, which will open a new project at the war table called A Way into Nyrissa's Dream. Once the time is over, you will be able to talk to the Storyteller and start the quest “The Path of the Dreams” where he will open the Dreamscape location for you and Linzi. There, Shyka will appear as a flashback/dream.
• Main Story: at the Castle of Knives in Chapter 7, during the quest The “First Crown”, you will stumble into the quarrel between the Wriggling Man and the Knurly Witch. Shyka the Many will soon follow, unlocking the achievement.
Credit to Starsong for their
guide.