Tap the "?" button at the top right corner to display the objectives in every level.
Leveling
After taking out enough targets, you can level up one of your character's stats (gun damage, melee damage, health). Consider improving your melee damage first, followed by gun damage after you have enough money to purchase a pistol.
Targets
Choose your targets depending on what you need from them. When short on money, target civilians. When short on ammunition, target the police. When going after a policeman, consider using melee attacks. If you try to attack them from a distance, they will shoot back with very good accuracy.
Travelling
To move around faster, explore until you find a random vehicle. There are at least three of them available on every level.
Weapons
Complete the first two missions to get the $1,000 required to purchase the pistol from the shop. It is safer than using melee weapons to take down your targets.