This pair of missions that make up the Extinction chain have you handling a race of Dinosaurs that have evolved to a space faring civilization. The Entity does not seem to be down with this development and wants them eliminated. This mission chain uses a combination of tactics from the Assassin and Best Friend levels.
Level 1 takes the method you learned in the Assassin levels and has you facing off against a lone dinosaur planet with only your own mass as a weapon against your foes. Even though the planet is evolved and shielded, a single collision with your asteroid will wipe off life from the surface instantly no matter your mass.
The idea here is to bait all the hostile red lifeforms into giving chase then circling about the planet at a fast speed until these enemies are on the opposite side of the planet, allowing you to safely turn in and collide with the surface. Perishing in this level is not penalized and will have you re spawning nearby the Dino system. For this reason you can also try just flying straight into the planet, however this is a matter of luck and timing, and can be somewhat hit or miss.
Note: Although covered in the main video below, the alternate video has a better strategy for the first mission only that is worth watching.
Extinction Video Guide
The second level in the Extinction chain now takes a page from the Best Friend level, having you pick you a secret weapon from a nearby location, that being a dark matter asteroid. Using the tactics you learned previously, you will need to push the dark matter asteroid along at a moderate speed in the direction of a nearby dinosaur solar system.
Whereas before you need to push an asteroid into other rocks, this time around you want to avoid other objects, taking your payload along without propelling it faster than you, preventing any necessary course corrections you might have to make via in-flight nudges. The path key is useful here to give some guidance for this purpose.
When the dark matter asteroid collides with an object it turns into a Black Hole, so make sure to pull back when approaching the target zone as you must survive not only until you demolish the dinosaur’s star, but also escape to a nearby beacon. If the Black Hole is triggered too close to you it will consume you guaranteed, however missing the dinosaur system and having it triggered somewhere nearby will still have a high chance of eventually pulling your targets in, so don’t give up if your aim was off, instead hang around and see what happens.