You can attack as part of a swing action. All the swinging rules apply normally. You cannot make attacks with two-handed weapons because to wield them, you’d need to take your hands off the rope (unless you have more than two hands, of course), but you can make unarmed strikes with your free hand or your feet/legs. To perform a Swing Attack, first, you must take a move action and make a Tumble check to place yourself adjacent to the target. Second, you must take a standard action to kick the snot out of him (i.e., roll to hit, etc.). After your attack, you are still on the rope, but you can drop to the ground as a free action. By the rules as written, this swing, Tumble, and attack are three separate, distinct actions, but you’re of course free to say that you swing up to your target, perform a mid-air somersault and catch him under the chin with your heel before hitting the ground like a cat. Even the most mundane attack can be enhanced through description.
You can also Spring Attack while swinging to strike your target in mid-swing. However, this incurs a -4 circumstance penalty to your Tumble check. If you fail the check, you can’t get yourself to within mêlée range of your target.
Finally, you can make a Swinging Charge. You get the standard -2 Defence and +2 to hit for a Charge, but you don’t have to move in a straight line. Instead, your movement is determined by the arc of your swing.