Just let the game take its course until you reach the table with the twins. After a few seconds, enemies will attempt a hit on you and you'll have to survive it while your boys drag you out of the firefight. If you have played other shooters before, the controls will be very familiar. If not, the game will offer you hints about the basics.
For the first part, you have to keep shooting the hitmen off your back. Take note that there's an aim-assist in the game, which allows you to auto-lock a target by holding down your sights (LT). You can quickly switch between targets by releasing your aim, pointing your crosshair to the next target and holding down LT again. This will help a lot in killing enemies quickly, thereby minimizing the damage you receive. Killing 25 enemies without dying or restarting a checkpoint will unlock the the “One Man Army” achievement. See the achievements section for more details.
Keep killing enemies until Vinnie successfully drags you back to the kitchen. Cutscene will follow and chapter ends.