Hey Elin,
This sounds like the perfect trip!
In addition to the awesome suggestions from Melin, I have a couple of ideas for the trip between Achill and Belfast. I've made this journey a few times, and each time I visited somewhere new. You're absolutely spoiled for choice.
If you're keen to see North Mayo (which is absolutely stunning), be sure to check out the Céide Fields. This is a lesser known attraction where you can explore pre-historic Ireland, preserved by boglands. It's an absolutely stunning spot, not far from the Downpatrick Head sea stack.
As you continue towards Belfast, you could also stop in County Fermanagh. I have a very special place in my heart for Cladagh Glen beside the Marble Arch Caves. There's a stunning stream that runs through the Glen with an amazing waterfall and so much green moss it's like you're in a faerie realm. :)
There are other roads and detours you can take between Achill and Belfast that would lead you to places just as beautiful and interesting. The good news is -- you really can't go wrong.
Excited to hear more about this trip!
Jenny