You'll be controlling a UNSC fighter as you make your way to the composer's location. Don't use boost that often; remember that if you pull your stick back, it will slow you down, making it easier to maneuver. You don't have to take out all the turrets; just the ones in front of you. Refer to the video below for the first part of this mission.
After reaching the objective point, you have to destroy the energy orbs powering the particle cannons. There are four and you can destroy them from the sides. Make sure to destroy the turrets along the way to avoid getting shot down. After destroying all the cannons, you'll be thrown to the next phase after the scene.
Destroy the drones since they'll be deploying forerunner auto-turrets. Head to the next hallway and continue clearing the hallways until you get to jump down the shaft. Head outside and insert Cortana to the pedestal. Enter the next few portals that she opens while defeating more enemies. Be careful of the enemy with the Incineration Cannon, guarding the next portal since it can instantly kill you even with full shields.
After entering that portal, you'll be thrown in the armory. Replenish your ammo or grab more powerful weapons then head to the next portal. The next area has more enemies, including one equipped with an Incineration Cannon. Take them out then enter the next portal.
In the next room, kill the initial wave of enemies and Cortana will have you defend the area as she hacks in the defense system. Eventually, she'll be able to override the defense turrets. Continue fending off the enemy attacks and retrieve Cortana when prompted. Make your way to the next portal while going through heavy enemy resistance.
Ride the lift up then proceed to the catapult. After reaching the central platform, resupply using the nearby ammo cabinets then proceed. Insert Cortana in the pedestal to update your objective. You have to overload the Didact's shields by sabotaging the two shield generators. Find the catapults leading to any of the shield generators and clear them.
Once you reached the platforms, you have to activate the light bridge first to reach the pedestal that will overload the shields. Make your way to the next catapult that will lead you to a platform with more enemies. Clear them out and make your way to the second generator platform.
After the scene, you have to jump to the next platform, eliminate a few more enemies then jump to the lift. Follow the lightbridge for a scene. After the scene, climb up and rush towards the Didact. Plant a grenade on him then crawl towards the bomb. Activate it and detonate it for a scene.