Oh man, I hate to tell you this. There are a lot of accuracy problems with the Handi's in .243.
Did you get the Superlight Youth? The one with the really thin barrel? These seem to be the most problomatic.
There are things you can do to help. All hope is not lost. First you need to head over to Graybeard Outdoors Forums and check out the Handi section. They do not have a good search function, but just read the FAQ post. It will tell you that you need to shoot a few boxes through the gun to break in the barrel. That you need to not rest the gun on the forearm, but on the frame and allow the barrel and forearm to float while firing. You will have to wait 15-20 minutes between shots. You also need to close the action very firmly until it breaks in. Try shooting the gun 3 shots with the forearm removed and the gun rested on the frame only, nothing touching the barrel. Make sure the barrel cools between shots. Then shot 3 shots with the forearm on and resting only on the frame and each shot from a cool barrel.
Try several differant ammo weights. The Handi's seem to be ammo sensitive.
GOOD LUCK! I gave up and bought a Remington 700.
Taken from GBO
http://www.go2gbo.com/forums/index.php/topic,116451.0.html
Handi Basics 101
1. Trigger pull must be all the way to the rear, don't release it at the break, or the transfer bar will drop out of place and inconsistent pin strikes will occur. See Misfires here
2. Close the action with some force, when new this is extremely important, the latch and latch shelf need to mate and that doesn't happen real fast, takes some open and close cycles for the parts to get used to each other.
3. Place the front rest just ahead of the trigger guard under the hinge, if you push the guard right into the front rest, it will be in the same position each time. On my rest, the rear sling stud is also against the rear rest.
4. Even after polishing the bore, it may take well over 60-80 rounds to start shooting well, my 223 Ultra started shooting real well after 80 rounds after polishing.
5. If you want to find out if the forend is affecting accuracy, remove the forend and shoot it, just slip it back on to reload and remove it again to shoot. If the forend needs work, it will shoot good without it.
6. Take your time shooting, most Handis don't shoot the best groups when the barrel is hot, specially without some forend work.
7. Always make sure the latch and latch shelf are dry, this is especially important if you clean at the range, it's real easy to get solvent on the latch shelf since it's directly below the chamber.
8. Make sure the brass and chamber are clean and dry, any lube left on the brass will make em stick, oil or solvent in the chamber will do the same.
9. With a barrel locked up good, the barrel release should be loose, the release should be snug with none or little looseness with the action open.