There are lots of 4-wheel autorickshaws which are available at the entrance (ticket counter) of Athirapally falls. You will have to pay the standard fare (do negotiate). No need to have your own vehicle.

As the previous comment has stated, early morning or around 5 pm should be good. Day times will be very hot.

Rs 15 per person and parking charge for car 10, van 15.

Entry Pass from Kerala Forest and Wildlife Department. Apart from that, I dont think there is any fee

Athirappilly falls would come first, so it must be visited first. For elderly persons, it could be a bit difficult to first climb through steps and rocky area to reach the origin of falls and then to go down through rough terrain to reach the base. Again one has to come back through the same route. However, at 71 I could do it with my one one leg having no knee cap due to fracture 28 years back and another leg having fracture near ankle 2 years back and also having undergone bypass surgery 14 years back. As I wrote in my review, several ladies with children in lap were also going down. I do not know the state of your parents but I would advise to go down the terrain at a low pace and must avoid any slip.. Certainly the beauty of falls can only be experienced by reaching the base. If you can do it with your parents in spite of some pain in legs (to be experienced for next 2-3 days as I had) that would be worth the trouble. The total time taken would be 1-2 hours depending on the pace of going up, down and up about 80 feet rough terrain. I also advise the tourists to wear shoes during this tracking.. Vazachal falls can just take 15-20 minutes only and even if one is late by 15-20 minutes, he can enter it.

Stay at Fort Kochi. Not near the falls. Use Uber for local travel as much cheaper than taxis.

You have private buses from Chalakudy private bus terminals. Share autos are affordable as well as the distance is only 5 kms.

You have private buses from Chalakudy private bus terminals. Share autos are affordable as well as the distance is only 5 kms.