These challenges unlock Destruction Mod gears. The general rule for this challenges is to destroy as much objects as you can through a series of explosions. Linked explosions will have score multiplier up to x8. If there are delays in your explosion combo, the multiplier will be reduced by half until it's back to x1.
Though there might be weapon restrictions for each Frenzy challenge, you're allowed to use any vehicle inside the area and use it to rack up points towards your goal. If you're having problems reaching the target score, you may try using better weapons / vehicles you'll unlock as you progress through the game. Also, explosions is the best way in racking up points; that said, any vehicle or weapon capable of launching rockets, missiles, or any explosives should be used, unless restricted.
Unlock by: Liberate Espia Bassa
Use an attack helicopter outside the base to build the multiplier. Start by destroying the antenna on the surface. Once you see it start to crumble, destroy the fuel tank, transformer inside the warehouse, transponder, and the three Doppler radars. Carefully fly inside the middle of the base and destroy the transformers and core units, then move to the fuel tanks. Finally, head to the remaining generators and use your grenade launcher to destroy them. If you have the multiplier going, you should have already reached the 5-gear score target after destroying the generators.
Unlock by: Liberate Puncta Sud
You can use the attack helicopters nearby but their minigun may prove to be a challenge to be used to destroy larger targets. However, it’s easier to rack up combos and multipliers. The mortar is powerful but you have to consider the firing arch and the delay of the explosions, as well as the range.