Yep, sounds like GKR - Taigyoku Nidan (usually just called "second kata" for some reason).
Personally I feel that is the one kata Mr S should not have changed, in fact it's IMHO the worst kata in the GKR syllabus.
But anyway...
1.Starting from the left foot forward long fighting stance (Zenkutsu dachi) bring the right foot forward until it is alongside the left one, keeping your left leg bent, and bending the right one as it comes forward. The gi trousers should rub together, so the leg has to travel inward slightly as well as forward.
2.Once the legs are level, raise the right knee, keeping the left one bent, and your body at the same height. Snap the foot out, and at the same time thrust your hips forward slightly, driving the ball of the right foot into the gut of your imaginary opponent's beer belly.
3.Retract the foot, keeping the knee up, then drop the knee down so you end up in cat stance (nekoashi dachi) then immediately slide the right foot forward as you straighten the left leg so you end up in a right foot forward long fighting stance.
4.Punch a split second before your foot stops moving, so the punch would hit the target as the stance sets.
Then do it again on the other side.
That's how I worked out looks best, although at full speed it still looks naff. Oh, and don't forget, when you're going to the sides it's punch then kick, when front and back it's kick then punch.
How do I know? I train GKR and Kyokushin. Previously Shotokan and Shorinji Kempo.