Cleaned the Mean Streets
This achievement is activated by taking control of a cop car at any point in the game, except in the middle of a mission, parking, then pressing the left bumper button to activate the police computer. This will show a list of crimes in progress, along with criminals that need to be apprehended. Capturing --- or killing) --- 20 total criminals will net you this achievement. However, if you've used the "full health and armor," "full health, armor and ammunition," "weapons 1" or "weapons 2" cheat at any point, it will not be counted, no matter how many crimes you stop.
Finish Him
The "Finish Him" achievement is gained through hand-to-hand fighting, a rarity in the main mission mode. The key is to execute 10 melee counters in less than four minutes. The most efficient way to do this is to start a fight with someone who's unarmed --- namely a pedestrian --- then press the "A" button to dodge his punch, and the "B" button to launch a counterstrike. However, if you've turned on the "full health and armor" cheat, you will be unable to collect this achievement.
One Man Army
To collect the "One Man Army" achievement, you must survive for at least five minutes with a six-star "wanted" level ---- the highest in the game. With six stars, the authorities will use all resources available to bring you down --- from helicopters, to FBI agents to Army tanks. Due to the difficulty of evading so many forces at once, it may be tempting to use cheats like "full health and armor" or "remove wanted level." However, both of these cheats will make it impossible to complete "One Man Army."
Walk Free
"Walk Free" is similar to the "One Man Army" achievement challenge, but instead of surviving a six-star "wanted" level, you must rid yourself of a four-star "wanted" level. While it may not seem as challenging due to the reduced star level, both surviving and throwing the police off long enough that they forget about you completely presents a host of challenges. Using the "remove wanted level" cheat seems like an easy workaround, but it will in fact make the achievement impossible to gain. The same goes for the "spawn police helicopter" and "full health and armor" cheat.