The <This Will Do Nicely> Galactic Seasons Objective can actually be done very easily, at level 12 on a Republic Character or at level 70+ for both Factions.
While many players get stuck and rely on farming Flashpoints or odd/slow locations, you can have the Objective done in under 10 seconds as a Republic character when you start the [Heroic 2+]: Republic’s Most Wanted on Coruscant.

To easily complete the Objective, set your best companion to either Heal or Tank spec, then run directly into the Heroic area without killing anything, turn left into the first room and you will see the Poison Canister ready to be used!
Run past it to the next room and aggro or use a ranged attack (saber throw, pistol shot etc) on the 2 Bosses and run back behind the crate next to the Poison Canister.
When all the mobs and bosses pool up around you, use your companion to protect you and explode the Poison Canister on the other side of the Box by right clicking on it.
In a matter of seconds all the mobs will die and the Season Objective will be completed!

If you don’t have a Republic character at least level 12, you can enter the [Story] Uprising: Firefrost as an Imperial (or Republic) character as long as you are at least level 70+.
From here, head down the elevators and pull as many mobs as possible, take them over to the closest Explosive Canisters and blow them up. The first 2 rooms of the Uprising with enemies have 3 total Explosive Canisters so there is more then enough Canisters to try multiple times if you don’t kill all the enemies on your first try.