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.
Unlocked by: Liberating Vis Electra
You just need to wreck as much as possible using the provided helicopter. Destroying chaos objects like fuel tanks, transformers, radar dishes, etc will rack up more points and increase the score multiplier. As long as you chain your destruction and keep the score multiplier up, you can get more score compared to individually destroying the targets. Even if your time is up, you can still continue destroying stuff until your score multiplier dies down.
Unlocked by: Liberating Cima Leon: Silo
There are three APCs positioned in the base and you can use their turrets destroy the chaos objects. However, since the counter will start only after the first destruction, you can use this time to prepare. You need to move the APCs to locations which will allow you to fire at more targets in a shortest amount of time.
For example, in this image, you can shoot the three transformers and the far satellite dish while also having the nearby fuel tank and generator in range. The second image below shows the APC positioned where your gun can reach the satellite dishes and doppler radar on the upper ground, as well as the transformers inside the tunnel.
You can watch the video below how you can easily get a 5-gear rank in this challenge using the setup described above.
Unlocked by: Liberate Le Tutor
In this challenge, it is recommended to use the Automat U12 automatic shotgun because of its fire rate and accuracy. From the starting position, target the fuel tanks first, then the satellite dish, then the next fuel tanks. Make sure you're in a safe distance away from the explosion to avoid getting thrown away or trapped by the flying debris. Move to the transformers and destroy one of the smaller ones to continue your multiplier. To destroy the larger generator, you have to destroy the ventilation fans to short it and make it explode. Don't forget to destroy the other two transformers beside it.
Once done, head to the Satcom dish area as fast as you can then destroy the two tower fuel tanks to retain your multiplier. Next, destroy the nearby transformers then head to the last transformer and generator inside the cavern.
Liberate Porta Vena
Like other Frenzy challenges, you have to cause as much destruction as possible within the time limit, using only the boat's onboard weapons. While the score for a few gears is doable with the default machine gun-equipped speedboat, it is recommended to use bigger and badder boats once you successfully unlocked them later on.
Unlocked by: Liberate Le Galera
Since there are three areas to wreck, you have to start in the generator blocks and destroy the chaos objects on ground level. After that, grapple to the top of the hillside level of the complex where there are more transformers and radar dishes. Once done, glide to the ruins are and destroy the objects there. You have to build the multiplier quickly and do your best maintaining it since it's the key to getting a high score and keep your extended time going even if the timer runs out.
Liberate Vigilator Sud
This is one of the easiest Destruction Frenzy challenges to get a five-gear score. What matters is the order you destroy the objects. First concentrate on the Satcom dish. This takes a lot of hits before it can be destroyed you'll start with it first. Next, build your multiplier with the radar dishes and the fuel tanks in view. Once you've reached x8, take out the antennas. From there, you should be able to reach the 20K point requirement to get 5 gears.
Liberate: Porto Le Gratia
There's an easier way to complete this challenge even without using the machine gun. There should be a parked CS Navajo attack helicopter on the landing pad near the base's seaside gate. You can use that to easily destroy the assets and rack up points way above the 5-gear target.
Liberate: Cima Leon: Transmitter
In this challenge, there are two tanks you can use, for each area. Now before destroying anything, position these tanks so you can easily destroy the targets without requiring too much re-positioning. You can refer to the screenshots below to learn some of the ideal positions where you can park the tanks for maximum coverage. Remember that you can destroy any obstacles without triggering the timer. As long as you avoid touching any of the chaos objects. Destroying enemy vehicles can also add up to the multiplier. Another sure-fire way of achieving the 5-gear score is repositioning the vehicles in the area and line them up so when you move the tank, you'll get the multiplier going by destroying them.
You'll have to traverse between two locations, you have to position the other tank near the cliff so you can easily yank yourself towards it once you're done in the southern area. Consider your tank's range which will help you prolong the multiplier. Refer to the video below for more details. Take note that some of the vehicles have moved deliberately.
Liberate: Vigilator Nord
In this challenge, you're supposed to use the Sniper Rifle to destroy as many targets as possible. Well, forget about that. There are two Urga Postolka choppers available for you to take and you can use that to destroy the targets instead. Remember that you can destroy enemy vehicles to keep your multiplier fresh. While building the multiplier, destroy minor targets first before destroying the larger ones to get more score. This should another easy challenge to get a 5-gear.
Liberate: Cima Leon: Centcom
No vehicles, no weapons, just your grappling hook and grenades. Unfortunately, your grenades are not infinite. First, you have to set up your tethers first. The grenades will be used to build up the combo gauge while the prepared tethers will allow you to trigger more explosions while the combo is high. I suggest tethering the targets on the central tower first then trigger your first explosion, preferably a fuel tank at ground level. As part of the preparation, make sure to remove most of the fences first that may block your tether cables.
Also, remember that destroying vehicles will add a bit to your score so arranging them in a way that they’ll get caught in the explosion while the multiplier is as its peak will help boost the score considerably. The long-range antenna will take more than one barrel to destroy. If you want, you can drag one of the FH155 heavy turrets back to the base and position it so you can shoot the chaos objects within your sight.