The Akamas Peninsula is a national park and UNESCO World Heritage Site. For millennia, the peninsula remains uninhabited and untouched, without any agricultural land. Tourists come here for 2 main purposes: hiking and relaxation on the beach. It will be difficult to combine both, as you cannot walk a lot during the hot weather. The ideal option would be a trip around the peninsula by car with stops on the beautiful beaches. Just keep in mind that roads there are bad, so it's better to rent a SUV.
If you are traveling by public transport, then come by bus #622 to its final stop, Baths of Aphrodite. Then your actions will depend on the weather. On a hot day, there is no sense in hiking. You can visit the Baths of Aphrodite, the goddess Aphrodite used to bathe there according to a legend. There's not a lot of space, so it can be crowded. Then go to the beach, which is located under the restaurant. This beach is not crowded and the water is clean. If you want to see the beautiful scenery, then reach the first turn, which is about 1 kilometer from the restaurant.
If the weather allows, you can walk along the hiking trails, the maps of which can be downloaded here. If you are not good with maps, then just walk along the sea, as we did. Be sure to take enough water with you as there will be only one water source on the way.
Another option is to rent a quad or a buggy in Polis. There are also organized quad bike tours. Be aware that the route from Paphos is completely different. Here are examples of routes: Paphos 1, Paphos 2, Polis.
In 3 kilometers from the Baths of Aphrodite the road will go down to the water and there will be deserted beaches. One of them is called Blue Lagoon and is usually crowded with tourists that arrive by boats from Polis. The water here is crystal clear, with underwater world and fish.
Getting there: Take the bus #645 "Paphos - Polis" (schedule, map), then change to bus #622 "Polis - Baths of Aphrodite" (schedule, map).