Here is the full list of all 21 Last Day of June achievements. It takes around 3-4 hours to unlock all of the achievements on Windows.
See the epilogue.
Accepted the truth.
Prevent the crash caused by June.
Deliver the gift.
Collect every memory of the Old Man.
Open the gate to the Graveyard.
Prevent the crash caused by the Hunter.
Collect every memory of the Kid.
Prevent the crash caused by the Best Friend.
Knock over four vases.
Prevent the crash caused by the Kid.
Peek at Carl and June at the Lake
Shoot the ball at the basketball hoop four times.
Wake Up.
Look at every viewable in Carl and June's house.
Try to involve Teddy in the surprise.
Give June a flower.
Listened to every diorama.
Pick every petal of a single flower.
Collect every memory of the Best Friend.
Collect every memory of the Hunter.