Hi Elin,
It's great that you have the time to take the road less travelled. :) When you start your trip in Dublin, instead of taking the M4 out of the city, take the N7 towards Kildare. That way you get to see the National Stud and Japanese Gardens for a nice walk, and you can stop over at Tullamore if you have the time as well.
When you travel from Galway to Achill Island you could take the road a little more inland, but this would mean you wouldn't pass Westport which is a lovely town. My recommendation is to take the
Great Western Greenway as it has loads to see and do along the way. You'll find many opportunities for short walks or hikes as well!
It takes about 7 hours to drive from Achill to Belfast. You can take the road through Sligo, as it has some spectacular views, and then follow the way into Northern Ireland.
For the drive between Belfast and Dublin I would definitely recommend sticking to the coast as it is more scenic. The two cities aren't too far apart so if you have the time, venture into the
Mourne Mountains as well. You'll find signposted walking routes all over the area that aren't too long.
Hope this helps!