Your first fight in the Ninja Escapades is probably the easiest one as well. The reason for that is fairly simple - Kakuzu isn't the strongest character, and Pain is way more effective than him.
Your enemy is a typical melee range fighter and it's there where he's the most effective - you should be extra careful about his grab, which has a deceptively long reach (and like any attack from that group cannot be blocked), as well as his Ultimate Jutsu, which he can grab you with from mid-range. The only worth noting ranged attack at his disposal is trivial to avoid - all you have to do is to simply jump away, or use your Chakra Rush and you will surely emerge without a scar.
Pain is extremely effective versus enemies who happen to be very close to him - you can use his Jutsu (Almighty Push) to stop any ranged attack fired at you, damage the enemy you managed to caught in it, and throw him a few feet back. This maneuver is especially effective when Kakuzu tries to overwhelm you with his attacks - all you have to do is to dodge his attack (use substitution to get behind his back) and active your jutsu.
If you want to receive a bonus, finish the enemy by using your ultimate jutsu.