If you did not follow the path 1 and you are just leaving the apartment, just go outside the building, walk left and at the corner (Piraeus Bank) take again left. Then you walk straight for almost 5 min, (you will walk towards the hill), you will reach the parking of Arvanitia beach (click here for the location) which is the end of the path 1.
and if we zoom in:
You will arrive at the parking area. Then you have to take the small path (path 2) which connects Arvanitia beach to Karathona beach.
The path will look like:
Usually it takes 20 to 30 minutes to reach the Karathona beach. It is a very nice path and while you are walking, you will be able to see many small hidden beaches that usually people do not know – where you can swim!