Important bits are:
Travel insurance, credit card and travel medication kit. Especially if you are a bit remote you should take Calpol, thermometer, plaster, antibacterial cream and stuff for insect bites.
Sun cream - you will need a lot, Greece is hot in August, we run out and found it difficult to get high factor suncream which didn't bankrupt us.
For swimming - get the UV suits, they will reduce the battle of applying suncream.
Hats, proper sunglasses
Beach towels for the pool, even if your hotel offers them, we always had our own, for DD we had hooded ponchos.
For the plane - if you have a tablet download whatever is currently their favourites and take headphones. Sticker books are good, read to them, pad and pens, a magazine. Lots of snacks.
DD had chronic constipation at that age and frequent leaks. She was still in swim nappies until she was 5. I had double the amount of knickers for her than we were away in days and travel laundry in a tube to clean accidents, washing out shorts and trousers.
Check the state of the beach, you may want to get water shoes if it's pebble. Sliders/flip flops for the pool area. Sandals for all day. We only had trainers on the flight out and back and when we did longer excursions.
I can't help with formula/baby food, we didn't do hotels at that age.
Baby carrier - it depends. What are your plans? If you want to do excursions I would say yes, it may be easier than having the pram with you.