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.
Collect every memory of the Old Man.
Open the gate to the Graveyard.
Collect every memory of the Hunter.
Collect every memory of the Best Friend.
Collect every memory of the Kid.
See the epilogue.
Accepted the truth.
Prevent the crash caused by June.
Deliver the gift.
Prevent the crash caused by the Hunter.
Listened to every diorama.
Prevent the crash caused by the Best Friend.
Prevent the crash caused by the Kid.
Peek at Carl and June at the Lake
Look at every viewable in Carl and June's house.
Try to involve Teddy in the surprise.
Pick every petal of a single flower.
Knock over four vases.
Shoot the ball at the basketball hoop four times.
Wake Up.
Give June a flower.