Three things you need to know about air rifle accuracy:
Any air rifle that shoots at over 900 fps or so is getting into the transonic region where some of the air moving over the projectile will be trying to break the sound barrier. This is VERY averse to accuracy. To avoid this, higher powered air rifles need to use heavier projectiles. To a limited degree, different brands and flavors within a brand offer a range of weight. To go a lot heavier though, the calibre needs to increase, hence the existence of .20 ,.22 and .25 calibre calibre air rifles. If you are looking for performance on larger critters, consider not getting the .177 calibre with the impressive velocity number. You will obtain better accuracy, and the heavier pellets will retain more energy at longer ranges.
Next, the single stroke cocking rifles, whether break barrel, under-lever, side lever, etc. are all spring powered rifles. A spring is compressed on cocking, and upon firing, this drives a piston that provides extremely high pressure air to propel the projectile. They almost all have the downside that the recoil while small, is difficult to manage. The problem is that after doing their main job, the piston rebounds and produces a forward recoil…so the gun recoils first in the normal direction, then a fraction of a second later, it recoils in the opposite direction. And all this happens before the pellet has moved a scant inch. There has been one spring powered gun that avoided this by using two contra-moving pistons to cancel the recoil, but you are unlikely to encounter this.
Essentially, spring powered rifles MUST be held a loosely as possible. Any attempt to restrain the recoil will not be consistent from shot to shot, and accuracy will be horrible. This takes a fair bit of practice, especially if you are experienced with (powder driven) firearms, which generally require a secure hold for accuracy, and to avoid painful recoil related injuries. I suspect that this may be the issue with the safari hunter mentioned above. Someone who shoots high powered rifles on a regular basis is not likely to appreciate how light a touch is needed for a springer.
Note that this issue is avoided with straight pneumatic powered “pump up” rifles. There are also expensive pre-charged pneumatics that use a tank to store enough air for several shots. The multi-pump guns are less convenient and straight pneumatic guns have a significantly louder report than spring guns. (the pressure in a spring gun drops dramatically before the pellet leaves the barely) Since low noise is one of the factors that leads to the use of an air rifle rather than a firearm, this may be an important consideration.
Finally spring powered air rifles are very particular about lubrication type and quantity. Petroleum based lube in the compression chamber will ignite under the high pressure produced. (dieseling) this leads to excess, transonic, velocity, and inconsistency from shot to shot, so is detrimental to accuracy. Especially the cheaper guns are often shipped with excessive oil in the compression chamber which will take several hundred shots to clean up…so don’t expect an inexpensive gun to shoot to it’s potential until it has "broken in’. One drop of special chamber oil every few hundred shots will be needed after that, and still the first few shots after oiling may have poor accuracy.