There are three candidates for the quickest gold stat award: Defence, Sniper and Ninja. I recommend Ninja, which can take a little longer but has longer benefits for the rest of the game.
Defence is all about countering enemy attacks. 100 are needed for the gold, and picking fights and doing drug busts, which are unlocked during the course of the police case, will give you this very quickly.
Sniper is quick if you're already familiar with the game or pick up the weapon combat quickly. After unlocking the drug busts, go to Kennedy Town and go for the Sun Yat Housing Complex raid. There will be 15 armed enemies here. Take cover and wait for one to move in closer. Move to the other side of that enemy's cover, then vault over for the disarm. Immediately move to aim afterwards for anyone directly in front of you; go for bodyshots to ensure the shots connect. Keep moving forward into cover, as the next group of enemies come from behind. Once 25 of 50 shots connect, you'll get the gold.
The final option is Ninja, which requires a bit more planning. There are two Jade Statues to pick up immediately. The first is seen during the first mission when you regain control in Mrs. Chu's kitchen. The statue is sitting right by the back door in plain sight. The second is in the temple, and the favor Ting's T-Shirts will lead you directly to it. It's sitting on the temple's altar. Continue doing favors until the job Amanda pops up; complete this and it will open up the Martial Arts school. Pop back in twice after the mission to get points to spend towards melee upgrades. Take both bottom options, ending in Leg Break.
Now we can get things started. Find a drug bust area as a source of easy thugs and use your new move. The Leg Break stuns them and opens up their back, leaving you to doubletap
for the instant takedown. This is an incredibly valuable combo for the entire game, and you only need to do it 10 times to get the gold.