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The current Build of GRA is using a temporary combat system. Several game elements have yet to be implemented, like the Cover System, Localized Damages and the Stamina Meter. The combat AI used by NPC will also be strongly improved later one.
Some places are more convenient than others to attack someone. Raising your Alert Level in a City Center's park is usually a bad idea. However, in a suburb area, you are safer. Moreover use your weapon' statistics at your advantage. For example, shotguns have shorter range than most guns, so while you stay out of range you can theoretically grind your enemy to death.
Buy some bandages or First Aid Kits before a fight. Going into cover before using any item is beneficial as using them will pass a turn. You may also come across some specific skill or stat boosting items that you may want to use before going into battle. Steroids can give a huge boost to melee characters for example.
You will often be confronted against impossible odds. When you're alone with a pistol, flee when intercepted doing illegal things by multiple ranged cops. The damage system is too unforgiving for heroic stands in the beginning. Getting out of an enemy's line of sight will slow him down, and changing sector will make most of your pursuers clueless. Use it to your advantage.
Keep an eye on your accuracy and your ammunition count when fighting. Pistol are specialized low damage weapons, the 9mm has a high accuracy, the Glock has burst shot, the Desert Eagle has high damage. Shotguns are high damage, close range weapons. SMG should always be used with the Burst Shot mode, good for medium range targets. Automated Rifles are good all-around weapons, good damage and above average accuracy.
Until you get your hands on a combat rifle, you should try to lay low. A high Stealth skill will help you in avoiding being detected. Some buildings in some sectors have very little chance of being searched by cops, so you can sleep and wait there, reducing your Alert Level in the meantime.