You should generally activate Unburden when you're ready to do a lategame sweep or put pressure on your opponent midgame. Since you loose the speed boost after you switch or gain a new item, you have to choose the best times so you can make the most of it.
I now present you some sets with all the Pokemon that could run Uburden powerfully. (An Unburden based Liepard isn't very viable, nor is Accelgor, since it's already fast as anything)
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Hawlucha @ Power Herb
Ability: Unburden
EVs: 252 Atk / 4 SpD / 252 Spe
Adamant Nature
- Sky Attack
- Swords Dance/Hone Claws
- Acrobatics
- High Jump Kick
Set up a Swords Dance or Hone Claws if you predict a switch, then hit em with a Power Herb Sky Attack to get that one big attack off while using up that Power Herb for the Unburden boost. Proceed to sweep with Acrobatics afterwards.
Sceptile @ White Herb
Ability: Unburden
EVs: 4 HP / 252 SpA / 252 Spe
Modest/Timid Nature
- Leaf Storm
- Energy Ball
- Dragon Pulse
- Hidden Power [Ice]
Bring out a Leaf Storm, heal off the Special Attack drop with the White Herb, outspeed and destroy everything in NU. Make sure to use Leaf Storm when you know you can get a clean sweep, as you don't want to be forced to switch and loose your boost. This is a set I use myself, and it puts in a lot of work.
Sceptile @ Liechi Berry/Sitrus Berry
Ability: Unburden
EVs: 252 HP / 252 Atk / 4 Spe
Adamant Nature
- Swords Dance
- Acrobatics
- Leaf Blade
- Earthquake
Even with little to no investment in Speed, Sceptile outspeeds all of NU and a lot of RU (even when Scarfed) after an unburden boost. You can intentionally not invest in Speed here to take a hit while setting up an SD, activate your Liechi Berry and get the attack and Unburden boost.
Slurpuff @ Sitrus Berry
Ability: Unburden
EVs: 4 HP / 252 Atk / 252 Spe
Adamant Nature
- Belly Drum
- Play Rough
- Facade/Frustration
- Thief
Set up a Belly Drum, heal off the damage and get the Unburden boost with the Sitrus, then proceed to sweep. Only go for Theif when you know when you're about to go down, or there's no way that you can kill whatever they send out, since gaining a new item gets rid of the boost.
Drifblim @ Weakness Policy
Ability: Unburden
EVs: 252 Atk / 4 SpA / 252 Spe
Lonely Nature
- Endure
- Acrobatics
- Knock Off
- Shadow Ball/Will-O-Wisp
Predict the supereffective move and go for the Endure to survive AND activate your Weakness Policy AND get the Unburden boost. While this one is harder to pull off, it can easily take down 1-2 mons with it.