Hand of Fate 2

Goblin chiefs are the large ones with a basket on their back and usually have an intro video. You can encounter them in Endless mode or in the Mapmaker adventure from the Outcasts and Outlands DLC.

They release a gnome who will launch at you. You can roll out of the way or they land on you and you have to bash Y to remove them. Either way, the gnome is then on the floor and you can kick it with LT.

Do this 5 times for each Goblin chief. Make note, sometimes you face 2 chiefs at once and it's hard to track which gnome is from each chief. I would kick 15 just to be sure. However, it will still only count as 1 towards the achievement.

The other 2 Solutions are good ones. Mapmaker is the way to get this. However, I felt it would be good for all to know that to get this quickly you should add as many Map Reveal cards as possible to your deck. This will allow you to skip past some of the Crimson cards. The staircase to the next level is also ALWAYS on the outside somewhere. When I was speed running through Mapmaker to get this achievement I would only go around the outside of each map until I found the staircase to the next level. Using this method (filling deck with Map Reveal and following the outside of the map only) I was able to complete each run in 10 minutes (sometimes less, sometimes a little more, depending on how lucky I was finding staircases).

Hope this helps!

Goblin chiefs are quite rare in endless mode. The easiest way I found is to complete the "Mapmaker" challenge, the other DLC. There is one garrantied goblin chief at the end. With a good deck, each run lasts less than 30 minutes. Focus on cards to avoid battles, with food/gold gain.

NOTE :
Even if there is several goblin chiefs during a fight, you will only gain the progression for one of them. I've put the tracker for this achievement on, and during a fight with 3 goblin chiefs and at least 30 gnomes kicked, I got only 10% progression.

Even if you quickly quit the game when you see your tracker progression have increased, you WON'T earn this achievement by doing the same battle over and over. It didn't work for me.