Did you learn how to stab? That's all you have to do. To stab, poke the wiimote forward. If you flipped it completely over on its back, you have to use the finishing move by swinging the wiimote and nunchuck forward at the same time.
if it's hanging, use the spin slash to spin the spider round, that will expose the purple weak spot which you stab
if it's on the floor, use the Flip Slash (or whatever it's called) to flip it over and use the finishing jump strike thing to obliterate it
If you have the Beetle, you can cut their web down so the Skulltulas are on the ground and crawling all around. Then, do an upward slice to flip over the Skulltula and they will temporarily flail around on their backs. Target-Lock them (hold Z) and it should flash saying "Final Blow" and do as it motions which, if I remember, is to move the nunchuk and the wiimote at the same time and you'll automatically kill the Skulltula.
If the Skulltula is hanging from a thread you must:
FIRST: Cut it down with the Beetle
SECOND : Either use a Verticle Spin (Slash the Nunchuck and Remote upwards) or a regular upwards slash (Slash the Remote upwards). Either one will put it on its back
THIRD : Z-target the Skulltula and thrust the Remote and Nunchuck downwards to preform an Ending Blow and kill it.
If the Skulltula is hanging from a thread and you can reach it you:
FIRST: Swing the remote either right or left to preform a simple right or left slash. This send the Skulltula into a spin
SECOND : Z-Target the Skulltula and WHEN IT'S WEAK POINT IS EXPOSED Stab it (thrust the Remote forward) Do this until it dies.
If the Skulltula is in a web FIRST: Cut it down, the preform steps 2 and 3 from tutoral 1.
If the Skulltula is just walking around do steps 2 and 3 from tutoral 1.
I also had problems beating the spiders in skyview temple...i died like 5 times i think... I didn't remember i could stab them until i remembered that i could...lol... But stabbing is quite difficult in that game sometimes Link just slashes left or right because when you thrust the wiimote it might go little bit left or right which makes link slash...you have to do it perfectly and thrust the wiimote straight...
If the Skulltula is on the floor:
1) Slash to the ceiling
2) Preform a Fatal Blow (if you haven't learn a fatal blow, go to the Sparring Hall at the Knight's Academy and practice on all the logs. You'll be taught the Fatal Blow after).
If the Skulltula is hanging by a thread:
There are two ways
A:
1) Cut down the thread with the Beetle.
2) Preform a Fatal Blow.
B:
1) Slash at it horizontally until you rotate it.
2) Thrust the Wii Remote forward to jab at the weakspot.
3) Jab a second time to kill it.
If the Skulltula is hanging on a web:
1) Cut the Web down with either your sword or Beedle until the Skulltula is on the floor
2) Slash to the ceiling
3) Preform the Fatal Blow
I hate these things too. My advice is to avoid them if you can. I would only kill them for fun if they're hanging off a thread and if I have the Beetle.