The palace looks deserted, so feel free to look around it. The only things you have to keep your eye on are the gas mines. To neutralize them use MG or just crawl onto them.
There are also anti-personnel mines [A]. You can shoot them or crawl onto them. Unfortunately, this time MG is useless.
While sightseeing you would spot some fancy laser traps. Stay away from it. For now - you can do nothing and even touching it would kill Snake.
There is an anti-personnel mine in the kitchen [A] and a tune for your iPod [B]. Before entering the top floor watch out for the last, hidden mine [C].
You would find there the Meryl's team's, Snake Patrol, hideout. And again you will meet Akiba, the guard who was hiding inside the barrel.
After a chat with Meryl Rat Patrol is going to be attacked by trained PMC troops. During the escape try to keep your position inside the group's formation.
Depending on the way you want to finish the game, you can help Meryl and her boys fighting the attackers or just watch how they eliminate them. They would manage themselves, but it would take much more time.
When passing the toilet room Akiba is going to be stunned. You will have to revive him. Stand above him, crouch and press the triangle button. Snake will tap him and with every tap the one star above his head should disappear. Using this method you can also wake stunned enemies.
Remember those fancy laser trap? Akiba would take care of it. After it's turned off - jump through the hole in the ground.
Soon one of the wall is going to be smashed by the bulldozer and another wave of the enemies would appear. Hide behind the counter and try to eliminate them. After the fight go with the rest of the team to the elevator.