1. Blow up 25 gang controlled vehicles in 60 seconds - Get the Firefly rocket launcher and the proximity mines (or if you don't have the DLC get the Cluster grenade). First go to the Shai-Gen territory and go to the Central Point tower (the second really tall one, NOT Wang Tower). Under it, there is a Shai-Gen parking garage. Now, piss off the Shai-Gen so they send hit squads after you. While they're coming, blow up this garage. Then destroy the hit squads. Pie!
2. Kill 15 gang members with your bare hands or thrown objects in 60 seconds - Los Muertos are the easiest because they have weaker weaponry. Stay away from the Volk for this; they use rocket launchers too much. Get 4-Star strength, then just head to a boss location, piss 'em off so they all come to attack, and have fun.
3. Shoot and kill 15 gang members in 60 seconds - MUST be with bullets, not rocket launchers. Use the Colby EAR50, Ingalls MG-60, or Harlington HMG-90 (*BEST*). Again, hit up a boss location - Los Muertos' kingpin is probably best - and rock it out.
4. Use explosives to kill 25 gang members in 60 seconds - Same weapons as the gang vehicles, except the Los Muertos kingpin is also a darn good one for this too.
5. Use any vehicle to kill 10 gang members in 60 seconds - This has to be RUNNING THEM OVER. Any vehicle that shoots, if you use its weapon to kill, whatever weapon type it is, the kill will count to that skill (gun = firearms, rocket launcher = explosives). You can ONLY kill them by hitting them. With that said, all three Agency cars are great for this. The Supercar, when upgraded, will plow under their cars and flip them up, killing them instantly. The SUV is pretty good for all-terrain, and the semi truck plows through everything. Find a crowded area and have at it. Easiest in the Central Point tower with the Buggy, though.
6. Pop 20 tires on gang-controlled vehicles in 60 seconds - Go to the Shai-Gen territory and find the Central Point tower (again). Under that tower is a Shai-Gen parking garage with 5 of their SUVs and 5 sedans. Go over to the SUVs (because they have six tires each) and take aim, then DON'T TOUCH the right analog once you're aimed. Just move your Agent along the SUVs while firing. Three tires on each side = really fast popping, especially since the tires are large targets. I recommend the Harlington HMG-90, but the other two high-capacity assault rifles (Colby EAR50 and Ingalls MG-80) are good too.
Piece of cake.