You'll regain the control over the main character only after reaching a blockade and getting out of the car. Do not try to explore the area because it may end with failing the mission. Instead of that follow Reggie towards the blockade. When the main character approaches Core Relay he will get a new power - Smoke Shot. Thanks to it you'll be able to shot projectiles similar to those Hank was attacking Delsin with. Aim at the Tracking Drone flying around and try to shoot it down (remember to target in advance because projectiles are not very fast). Shooting down the drone will result in new cutscene where you'll talk to Reggie.
Approach the destroyed drone and press touchpad to collect firs Blast Shard. Shards are used to develop Delsin's powers and there are four of them in this area. Unfortunately shooting three more drones is not possible right now and that's because Delsin has used his smoke. The game will teach you now a very important gameplay action - absorbing smoke to regenerate main character's powers. Just look for places with visible smoke. Look around and approach one of nearest wreckages to absorb the smoke (press touchpad).
Now you can start attacking three other drones - two of them should fly over the yard and the last one should be attached to the destroyed fragment of the barricade. If you use your smoke in the meantime (Smoke Meter in the left bottom corner) approach one of wreckages to refill it. Make sure to examine each destroyed drone and get Blast Shard. Leave the location only after getting all four shards. Move to the bus and try to use Smoke Shot on concrete barriers. You'll fail so press Options button in order to open the Powers window for the first time. In this particular case you have to spend four shards on unlocking Cinder Blast.
Position yourself near one of concrete barriers and hold R2 to perform Cinder Blast attack. Once you destroy the barrier go to other concrete elements and use Cinder Blast on them. In the meantime do not forget about regenerating your smoke (nearby car wrecks). After destroying first group of concrete elements wait until bus drives to a new place and destroy a larger barrier. The game will show a cutscene with Delsin and Reggie - brothers will decide to split up for some time (the mini-map of the area will be also unlocked in the right bottom corner).
Use the previously destroyed passage and after a while you'll get to the tunnel entrance. There are several armed bandits here and you'll have to fight a battle with them. You can mainly use the Smoke Shot against them, which allows you to keep enemies at the safe distance from you.
Note - if you use your smoke you can attack one of cars in the tunnel with your chain - smoke will begin to float out. The advantage of this method is that you do not have to look around for car wrecks.
Alternative method of eliminating bandits is getting close to them with usage of Smoke Dash and using the chain on them. The last enemy will try to surrender and once again you'll have to make a decision associated with karma. If you want to get Good Karma you'll have to subdue him (triangle button). But if you want to get Bad Karma, you have to kill him (square).
Note- Throughout the game, you will be encountering many of the enemies that will also try to turn themselves in (especially if they are the last on standing in the battlefield). Each time, you will be allowed to decide whether you just want to kill or immobilize them (you can ignore taking such decisions, which are concerned with karma, but you will then receive neither good or bad karma points).
Regardless of your decision, go to the tunnel exit coping with limited visibility. Once you get outside the game will show a short cutscene and you'll have to make your way over the heavily damaged bridge. Move forwards and stop at the new Core Relay. Press touchpad in order to unlock new Delsin's power - Car Boost. The game will force you to use it right now. Jump over the car roof and press X to bounce from it to get to the higher level of the bridge.
Keep going, using Car Boost in places where you have to reach higher bridge levels. After few moments you'll find one more Core Relay. Press touchpad to absorb its energy and unlock new power which allows you to float above the ground for a moment. It is done by holding X button and you have to use it in order to pass by first water reservoir. Keep going and use the newly acquired power when needed.
Stop at the end of the current bridge fragment - there is bigger water reservoir in front of you. You have to use all unlocked powers here in order to safely get to the new section of the bridge visible in a distance. Start with jumping over the car roof and bouncing from it (X). Once you're in the air press circle button (Smoke Dash) and start flying by holding X. If you do this combination properly, you'll be able to get to the new bridge section and continue your march.
Once you land on the bridge quickly repeat two last steps of the action combination (you do not have to bounce from the car roof), because the current bridge fragment will soon fall down. Reach subsequent platform using bouncing from car roofs and floating over the ground. Soon the game will show a short cutscene where you'll see that Reggie needs help. Turn left and get to platforms right there, so you can approach Delsin's brother and save him. Watch longer cutscene which ends this stage.