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.
Deliver the gift.
Accepted the truth.
See the epilogue.
Prevent the crash caused by June.
Listened to every diorama.
Open the gate to the Graveyard.
Collect every memory of the Old Man.
Prevent the crash caused by the Hunter.
Collect every memory of the Hunter.
Give June a flower.
Prevent the crash caused by the Best Friend.
Collect every memory of the Best Friend.
Collect every memory of the Kid.
Prevent the crash caused by the Kid.
Peek at Carl and June at the Lake
Knock over four vases.
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.
Pick every petal of a single flower.