Ingame
You can manufacture; make it a goal to have certain furniture or design your tent or make items to sell, lvl alchemy; then later compound stuff probably make it a goal to get a certain equipment for your chara or compound random stuff to sell, go questing; try and make it a goal to do all quest on each island/continent or get all pets you can (without really begging for help of course. that's the point of it being a "goal" certain hard pets like fred, venus/Athena/ joan etc.. that you may find too hard to do then get help.

maybe even make it a goal to kill all pets. lol I did that once. kept only the one I like (which was Fred at the time) I made up this story where Fred and I (the character) were going to rule the world and avenge Niss and our dead parents. and we had to collect the constellations and each would line up and form some new constellation which would open a gate or a map and point a way to becoming the ultimate pet so I had to kill every other pet and he and I would rule together muhahahah =.= see that's what boredom can do for you. you find ways to have fun in the game. also you can meet someone in game to be friends with and keep you company. some times you find your self lost for hours talking about stuff in game or stuff you have in common.

out of game
since its an afk game where you can just set up your remote and leave your chara to train or collect on their own (checking once in a while to see if anyone has died or even to check if you have mail, who's online you can talk to or w/e). you could probably even find a book to read or even go online and find some free e-books, or fan-fic or even manga online to read if you have nothing in hand, fine another game to play if your computer can handle it or play a game on a consol if you have that instead. or even watch shows or movies on your computer even spend a day lost of the crazy side of Youtube. start witch searching music vidos end up watching cats pwning dogs to even how napoleon icecream or hotdogs are made. Or get lost on a on a meme, joke or art site.

just google things like "watch movies online" or "watch tv online" etc... and then find a website to stream shows or movies you like or any show you've always wanted to see. if you don't have any shows to watch then google that too. "highest ranked movie or tv show or anime etc.." to give you a start of what to watch.

these are a start.

you can also go out and have fun too while your chara trains. don't need to spend boredom sitting at home. if you are going to stay inside or outside then you can also think of things to so in your own house as well. play with a sibling, spend time with a parent, learn to bake or cook or sew or draw or write or design or hack the white house or clean or do a sport...