Combat Zones in Elite are considered an endgame activity; especially so since about 2 years ago they allowed higher-level NPCs to have engineered modules, and their AI has been significantly improved. Military-type ships - that is, the ones you usually face in a Combat Zone - have also been equipping more heavily reinforced armor compared to the past, making them tankier.
You did not mention engineering in your post, so I'm assuming your ship is not engineered; while time-consuming, engineering will improve your ship's performance manifolds: your damage output will go up roughly 50-60% (depending on weapons and blueprints), and your ability to withstand damage will more than double.
Having said that, there are a number of things you can do, even in a small ship, to improve your odds.
Your turning speed is affected by your throttle position (with Flight Assist On) and your pips to ENG (with Flight Assist either On or Off). Keep your speed in the blue zone to improve your handling.
Engineering your Thrusters will also help, as does boosting. Since turn rate is increased in Flight Assist (FA) Off, many players switch to it, boost, turn, then switch back to FA On.
Of course using FA Off permanently will greatly increase your time-on-target, but it does have a steep learning curve.
NPC pilots in a Combat Zone (CZ) will tend to prioritise players, however you can mitigate this in several ways:
- Attack ships on the edge of the furball, not right at the center;
- Attack ships that are already being attacked by allied ships, possibly bigger than yours;
- Take pauses from time to time to recharge shields and pips; enemy aggro is based on damage dealt, so keeping a low profile for a while will make it less likely for nearby enemy ships to switch on you.
You also don't need to be at max speed all the time, especially if nobody is firing at you or your current target is attacking someone else; just slow down and match your speed to it.
Still, sometimes things may go wrong and it may be time to leg it; when that happens, fire a Chaff (because you have Chaffs, don't you?) and run away while rolling and strafing in either 4-2-0 or 2-4-0 configuration, depending on the speed of your pursuers. The small size of your ship will help avoid shots.
Newer players may not be aware, but having more pips to SYS does more than increasing the recharge rate of your capacitor, it actually makes your shields more resistant to all damage sources (including Absolute damage); the increase is slightly exponential, but peaks at a massive 60% when having 4. That is, an attack that normally deals 100 damage will only deal 40 damage if you have 4 pips to SYS at the moment when the attack hits.
Conversely, turn speed is affected by the amount of pips you have in ENG.
It is very helpful to change pips configuration on the fly as needed, I use a program called AutoHotKey to write pip-management macros.
Find a partner
It may not be easy to find one, but if you team up with another human player you won't have to share your earnings: if you are in a wing you both will get full credits for every target destroyed, assuming you both dealt damage to it recently.
Having a large ship can help; they take more punishment, they can equip Ship-Launched Fighters that are great for distraction, they have plenty of internal slots for Shield Cell Banks and additional armor, and they can spend all day in 4-0-2 for maximum lazyness (if they constantly reverse-turn to keep their aim on target). This is how I started, even before engineering became available.
You can consider saving up credits to buy one, or alternatively start engineering your ship - or both, as a fully-engineered large ship is effectively unstoppable in a Combat Zone.
Source: I'm a Flight Instructor for Spear, a PvP group comprising over 12 different Squadrons.