Gun that suits this needs

The HW95 on the banner at the top of this page.

"c_m_shooter"The HW95 on the banner at the top of this page.

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Every time I see that I get a tingle in my credit card.

I'm with CM . HW 95 is HARD to beat . IMO there are probably better springers out there for what you want , but you gotta make a BIG jump in price to get to them .

HW95 would be a great choice, but I would think about going used. Oftentimes, you can get a tuned used one for the price of a new one, and not even have to break it in. Since you can't be so picky used, here are some other options:

Beeman R9 - Almost the same gun. No sights, slightly shorter barrel, slightly different stock. Usually more expensive.

Tuned Xisico from Flying Dragon - Not the same build quality, but as they're tuned, you won't have issues. 

I wouldn't discount PCP, either, like a used Marauder in .177 or .22. 

Used Beeman R1

Walther LGV Ultra - newer technology, better tuned from the factory, and quieter than the HW95/R9. A little more expensive I think, and the styling is more modern.

I know you asked for break open but if you are not opposed to a side lever (see what I did there..) then the RWS Diana 48 or 52 are in your budget,magnum power and very accurate. The benefit with side or under levers is not having to worry about the barrel lock up.

I'm getting really attached to my Diana 340 N TEC. But it's the compact version. Pretty darn accurate and light enough to carry in the field. The version they sell now can't be much heavier and may even be lighter without the barrel weight/baffle of the Compact. I'm not that experienced yet with springers but the 340 gas ram has a pretty smooth shot cycle. But then it was tuned.

Check the HW prices from Krale, irrc my HW80 was $370 to my door. The HW 90 was around $400 + shipping

https://www.krale-schietsport.nl/en/guns/air-rifles.html?manufacturer=262

I've repeated this several times, Hatsan 125 in various stocks meaning various prices. All with the same power plant the 125th is the cheapest.