On a more serious note, Jimbo’s tips are pretty much guaranteed to save you the pain of extensive fragment farming.
Just in case you’re like me and you like to create a new character from time to time and start from scratch, here’s a bit of advice: start incorporating the Unnamed City fragment chest run into your routine as early as you can. You don’t actually have to fight a single boss to get 10+ fragments a day.
And when you’re ready to start leveling your first good follower, Unnamed City is a great place to do that, because of the XP you get from the undead there. So while you’re doing that, you might as well kill the bosses to get additional frags.
Also, the Unnamed City is not the only place to get fragments. There are fragment chests in the Wine Cellar, too. Also, harvesting the corpse of the Scorpion Queen in the silver mine will get you a fragment. There are other ways to get fragments, so I would encourage you to explore a lot 
Hope this helps a bit.