In the latter part of the Hong Kong Massacre campaign, you will run into elite enemies. This page of the guide explains how to kill enemies wearing bulletproof vests.
Enemies wearing bulletproof vests start to appear for the first time during the fourth chapter of the game (Yesterday), or to be more specific after starting the Big Trouble in the Secret Drug Lab.
Not every enemy you meet from that point on will be equipped with a bulletproof vest. You can recognize those enemies by their white shirts and black vests (as shown in the above screenshot).
The only way to kill an enemy wearing a bulletproof vest is to hit him twice. This requirement applies to all weapons. Even if you are using a powerful shotgun, a single shot will not be enough to take out the enemy.
The enemy wearing a bulletproof vest will always perform a roll once he is hit for the first time (as shown in the above screenshot). Once he finishes the roll, he will shoot towards the character. You can either hit the enemy the second time before he manages to perform the roll or move away a little after the first hit and wait for an opportunity to perform the second attack.