We need to develop a standard Springer NOT Grouping Check List
(maybe others can add to this)
1. check all the screws including scope screws (snug them up, and locktite them if they keep loosening)
2. tissue test (possible breech seal issues)
3. chrono the gun (is it consistent? if not, look at piston seal, spring, excessive lube to no lube, )
4. Troubleshoot possible scope issue (Shoot open sight to check if the scope is busted, swap scopes, mount a laser then use your scope to double check POI shifts).
5. Clean your barrel
6. Try quality pellets, Crosman CPH, CPL, JSB, H&N, RWS, etc, Try different weight pellets
7. lighten your trigger (be careful with this one)
8. Tune/detune your rifle (detuning might make it more pleasant to shoot and help you manage recoil thus shrinking your group)
9. Try the artillery hold and try not to shoot your gun resting on a solid rest/tripod (a hand under the forearm, softer padding? might help). Really be consistent on your position and trigger control. Shoot at 10 yards first to get good grouping before going to longer yardages. For me, if I can't group 3/8" at 10 yards, I tweaks things until I see good groupings.
10. check your crown
11. ? (I'm sure others will chime in)
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edit
I just did a quick google on that Beeman 1000 series. What version is yours? the dual caliber version?
As I recall, accuracy reviews were not stellar.
For most budget break barrels if you are looking for 3/4 to 1/2" at 25 yards ...it might be hit or miss (mostly miss, pun intended)...unless you want to do a ton of work on the rifle like swapping out barrels, polishing the barrel, crowning the barrel, tune the rifle, hone the compression tube, size the piston seal, modify the trigger, stone the trigger surfaces, install a tighter spring guide...and on and on.Allow me to correct the first and last steps.