Part 1
After the Albatross is destroyed, you appear in a new scene. Run to the right and grapple swing over the first box. On the other side, you will finally meet Hal at location A. It looks like Hal is in bad shape, but he hands you the Bazooka just before he expires. He tells you to use it on the helicopter below. The Bazooka is not actually a new unique weapon, it simply replaces your weapon with something like your Rocket Launcher temporarily.
Beyond Hal, you must grapple swing over the second box and begin falling down into the area below. As you fall down, the helicopter will come into view. The blue glass of the cockpit will stand out considerably against the yellow exterior. This is where you must fire your bazooka shot. You only get one chance to hit it. If you miss and land on the ground below, the machine gun mounted on the underside of the helicopter will defeat you with one bullet. Be sure to fire when you reach location B, and are lined up with the cockpit. If you are successful, the chopper will begin to explode, and you will witness the destruction of the resurrected leader. However, your mission isn't over yet.
Part 2
After the chopper is destroyed, you appear at the bottom of the map shown to the right. After you walk forward briefly, a message will broadcast that the base will self-destruct in 60 seconds. In that time, you must make it from the bottom to the top where a rescue chopper is waiting.
Start by firing your grappling hook upward and climbing up to each successive platform. At location C, the path will diverge. While the platforms on the left are grouped closer together, you will actually travel up the right platforms faster since there are fewer to climb. However, once you reach the top, you will be forced to drop down and catch one of the left platforms in order to continue your ascent.
When you reach location D, you will engage one of the large cyborg bosses that guarded some of the cores. Although continuing to the top is easier if you remove this opponent, you are not required to defeat him in order to proceed. In fact, it is recommended that you ignore him if you have any weapon other than the Rocket Launcher or the 3-Way Cannon, since fighting him may take too long. It's also possible to take a knockback from this cyborg for a shortcut, if you have an extra health bubble to spare.
Whether you choose to fight the cyborg or not, the best way to proceed to the remainder of the platforms near the top, is to stand on the far right edge of the platform just above the cyborg, fire your grappling hook straight across to the platform on the right, and then press 
to reel yourself in. You may end up flying too far to the right and hit the wall. If you do, quickly fire your grappling hook straight up in order to catch the platform before you fall too far. Then climb up the few remaining platforms before time runs out.
If you are successful, you will see the ending of the game, followed by the credits, and an epilogue to the story. Congratulations.