The only entrance into the sushi restaurant is through the front door, but there are some guards in front of it. Bentley suggests using the Samurai armor to "relieve" the guards of their duty, so equip it and walk up to them. The guards will leave and Sly will use his shield to launch Rioichi into the restaurant, who you will now be controlling.
Once inside, climb the plant and stand on the next point, then hold R2 and press X to use the Leaping Dragon technique to launch yourself to the next point. From the first point, you can launch yourself to the right side to find a Secret Sly Mask. Get onto the middle structure, then launch yourself to the other end of the room. Shimmy around the corner, being careful of the spotlight, then drop down into the room. Be very careful of the plates on the floor, as this will alert the guard and you will fail. Wait for him to fall asleep, then hurry past him and pickpocket to grab Rioichi's Carving Knife.
Open the door using the knife, then use the Leaping Dragon technique to get over the lasers. Sneak past the guard in the next room when he's sleeping, then use the trampoline to get onto the pipe above. Use this to get behind the next guard and steal Rioichi's Fillet Knife, then unlock the next door.
Stand on the bonsai tree, noting that it will break after a while, and launch yourself when you have a clear path past the lasers. In this next room, avoid the guards and climb the tree in the middle of the room, then use the points to launch yourself around the room to a platform that you can use to drop down. There's another set of lasers here, with more bonsai trees used as launch points. Steal Rioichi's Cleaver from the last guard, unlock the door, then pull the lever to finish the job.