Here is the full list of all 13 Connected Hearts - Visual novel achievements. It takes around 0-1 hour to unlock all of the achievements on Windows.
Read the credits
Complete story of Mary
Complete story of Royer
Complete story of Henry
Find Henry for the last time
Find Royer for the last time
Find Mary for the last time
Got the ending - Dream again
Got the ending - Happy Forever
Got the ending - Connected hearts
Got memories of Mary
Got memories of Royer
Got memories of Henry