The go-to advice for this one seems to be 'wait until you're level 55 so you unlock the Unforgiving passive, that enables Fury regeneration and doesn't allow Fury to degrade.
To that, I say balls! This is really quite easy to do at low levels. All you need is five minutes of your time, obviously, as the achievement requires you to fight with a full Fury gauge for five minutes and a lot of mobs.
Also note, hitting breakable containers such as coffins, tombstones, rock piles, rotting logs, stumps etc will contribute to your Fury gauge.
If you're a lowbie wanting to try this out, I recommend heading into the Weeping Hollow. Start at the bottom left (or right) work your way up the top, cross over to the other side, and start heading back down the other side.
Remember to just use your Fury generating abilities, and nothing that costs Fury to use. You will have approximately ten seconds when the last mob falls to start hitting something else before your gauge starts degrading, thus voiding the achievement and your hard work. As soon as you kill a mob, start looking for the next one, or a container to hit - there are plenty. When you reach the top, hold shift and whack some tombstones - whatever it takes to hit something that generates Fury within ten seconds.
Honestly, in The Weeping Hollow, you shouldn't have too much trouble with this. If it moves, smash it. Hell even if it doesn't move, smash that too. You're a Barbarian, it's how you roll.
Hope this helps someone looking for advice on this one.