Strafing: In a heavy firefight with 3 or more enemies, Mike's strafing ability will really come in handy. Use it to dodge incoming bullets, or create a 'line of fire'. This special ability can save you a lot of health/armor and time. Use in tandem with the Flamethrower to become ultimate.
Sprinting: Sprinting is just a quicker way of getting around on foot. However, Mike can only sprint for several seconds before tiring out. To counter-act this, complete Level 12 Paramedic so Mike can sprint indefinitely.
Jumping: If there's a barrier or a wall blocking your way, jump it! This strategy will work on most obstacles, and you don't need to activate jump to get over cars, because Mike will do it automatically.
Bailing: Car on fire? Heading towards the water with no hope of regaining control in time? Bail. In GTA Advance, you don't have to completely stop your vehicle to get out, which will save you time and sometimes health. An interesting thing to note is that when you bail out, your car will never come to a stop outside your field-of-view.
Horn: Although this function does absolutely nothing to help your game, it's fun to just beep it once in a while to annoy people who just beep back at you... Or you could pretend you're making a movie by starting a car chase with the cops and beep at everyone that gets in your way.
Activate Car Bomb: Activating it just puts it on standby, ready to blow up with a press of the detonator. Note that if you go too far away the car will be cleared from memory, making the carbomb unusable (you'll be told you're out of range). Having the car just on the edge of the screen should be sufficient to be clear of the explosion. Vehicles required for story missions will not vanish no matter how far you get from them (unless a certain distance from the vehicle is a criteria for mission failure) so installed carbombs will remain in the vehicle until the mission ends.
Handbrake: If you're heading towards a very tight turn, you might want to use the handbrake. It'll lock up the back wheels and let you turn tight corners easily without crashing into walls. Another benefit is that you can fishtail to look cool, do burnouts and perform donuts.