2003 Hyundai Tiburon clutch

Undo the bolts on the torque converter and hope you haven'tscrewed up the oil pump. Make sure the starter is out and you have the engine supported otherwise it's gonna try to come with trans and probably fallout. You should really get a manual for this to take this out because they recommend unhooking a lot of stuff prior to removal. Inluding axles and wheel spindle on drivers side.

I assumed because you didn't state whether it was manual or automatic

If you have a torque wrench then by all means use it if not nice an dtight will do just not overtight. To break the bolts. Case to engine mounts 63-67 Nm or46-49 ft lbs. Here is install instructions.
Insert the snap ring pliers under the wave washer to release the bearing.
Replace the clutch components as necessary by following the steps in the appropriate Shop Manuals.
NOTE:Do not attach the new release bearing to the clutch cover.

Install the release bearing on the fork as shown. See Fig. 7.
Fig. 7: Installing Release Bearing on Fork
Attach the clutch cover without the release bearing to the flywheel while the clutch disc is aligned using the clutch disc guide tool (refer to the appropriate Shop Manuals for the clutch disc guide tool part number).
Attach the transaxle assembly to the engine assembly.
NOTE:Make sure not to apply any side loads to the clutch components.

Install the release lever on the release fork shaft by aligning notches (release lever attaches only one way on the shaft).
After completing step 15, pull the release lever to engage the release bearing into the clutch cover fingers. If there is a click sound, the release bearing and the clutch cover are aligned correctly. If the assembly does not click and snap into place, the release bearing and the clutch cover are not aligned correctly. Repeat steps 13, 14 and 15.
NOTE:Do not apply excessive force on the release lever to engage the release bearing.

Reconnect all removed components in the reverse order of removal.
Add the specified amount and type of oil into the filler hole (refer to the applicable Shop Manuals

When removing transmission, Make sure to disconect the clutch fork arm completely, 14mm nut.

Remove completely or the trans will not release from the engine.

This is a pull cluthch type assembly.
Tighten clutch cover bolts to 11-15 ft lbs or 15-22Nm
Tighten the bolts by one or two turns at a time, in succession, to avoid bending the cover flange
tighten diagonally

Sounds like the clutch disc wasn't aligned properly there should be a plastic spline that you can get for about $5 to align it then tighten the pressure plate you'll have to loosen the plate again then the trans should go right in unless there is a trans bearing or bent spline but that is almost impossible to do

No the way it is in instruction is way to do it there isn't another way

That's the same question I answered previously it has to be put on with the transmission prior to putting trans to engine.

Unfortunately no it hast o come back apart.