Do it, do it and do it!
Sneakers, sweatpants and do it!
It is worth every drop of sweat!
When you get to the top of the mountain and see complete Naxos around you, and sea surrounding you, you will cry!
Please, be aware that this is not for kids. After the cave (which is nice, btw, but you don't have any light inside, so bring flashlights with you; this is not a maintained cave), you practically won't have any paths, but a lot of slippery rocks on a steep surface. It requires skill, balance and being fit.
For those who never did trekking and so on, follow the red circles/dots/signs which you'll have here and there, hardly visible, but they will show you your way.