You can earn these upgrades at ANY time just by going into a target-marked training facility and turning in a badge. You earn badges by doing random missions or regular missions. Note that you lose badge points when you get killed or do bad actions.

Upgrade 1 - dual target aim
Destroy 8 targets, avoid civilian targets that drop down.

Upgrade 2 - firing aim assistance
When aiming, it turns green to hit neutralizing point, red when hit lethal point. use press down R to do aim. You have to hit 8 times.

Upgrade 3 - fast reload
This is a great one, obviously quite helpful in any situation :)

Upgrade 4 - Fast Aim Speed
Another great one, anything that helps you aim more quickly is good in my book! Destroy 12 targets with no headshots or civilians. There are only 13 targets available so just blast away quickly, don't bother aiming much.

Upgrade 5 - Laser Sight
I didn't find this one very helpful at all, but heck, you have to go in order. Just shoot 10 targets for this one.

Upgrade 6 - Flashlight
This is an OK upgrade but not one that I needed a lot.

Upgrade 7 - Scope
An OK upgrade in certain locations.

Upgrade 8 - Top Accuracy
THIS one is well worth getting, it gives you a 50% reduction in aim error!

Shooting Training Areas
Central Street
Figueroa street & 9th
Alemeda north of 6th St
Melrose and Stanley (between Hollywood and Beverly Hills)
LeBrea and Melrose
Pacific and Washington 3rd & Olive in downtown

True Crime - Streets of LA Walkthrough


True Crime - Streets of LA Review