By the power of truth, I, while living, have conquered the universe.
Shortly after Halo 3 after the death of the Prophet the Covenant were in frantic confusion.
With no worthy Prophet to take the throne a powerful Brute Cheiftain took the throne by force.
After his rise to power he forsaked the Covenants original Journey to activate a Halo and focused solely on punishing the humans for what they have done, since he is a brute and has no interest in going on a religious journey and only wants to cause pain to all mankind (which is incorrect).
He uses the entire force of Covenant to full out attack earth. After a while the Covenant prevail and take out earth's outer defenses. Even though the Covenant has sustained heavy loses they still have enough forces to Glass all of earth and wipe it from the face of the galaxy.
He instead tells all forces to invade Earth again but this time full force and in multiple locations.
The UNSC is struggling against the force and is losing but only slightly a battle (wtf?). Lord Hood is notified of a beacon located about where the Cheif was assumed dead. He sends a few ships from one of the remaining outer colonies to investigate.
They come back with seven spartans, one of which is the Master Cheif. The other six were trapped on Onyx but are now freed and are ready to fight (major plot hole and makes no sense). They are given more updated armor and nicer weapons. They are sent in to Chicago to stop the attack on the city which is being slowed only by a force of ODST's lead by Buck, Dare, Micky, Dutch, Romeo, and the Rookie (would be a higher rank). They are almost pushed out when a strike ost (ost?) pushed all the way out and overun when a large strike force headed up by four spartans flanks the force and overuns them.
The other three Spartans, one of which is the Cheif, are pushing a strike force of Brutes out of D.C. After they push them out of Washington they move on to Boston and the other force moves on to Los Angeles.
After they have cleared the Covenant out of most of from the United States' largest of cities they move on to Europe (Just like that, huh?). They get the Covenant out of most of the European cities and then the Brute Cheiftain decides that the only thing to do now is Glass the entire planet (why not do it in the first place?).
While the ships are moving into position the Arbiter and his force of ships return just in time and engage almost all of the ships into a heated space battle (Super plot-hole = fail). During this time Lord Hood gets the Anti-Air rail guns (MAC guns!) optimized and uses them to sway the battle in the Arbiter's favor.
Three of the Spartans, the Chief included, assault the Brute Cheiftain's main command ship. During the attack they face the Brute Cheiftain. During this final battle the Arbiter finishes off the rest of his fleet.
During the fight the Cheiftain manages to kill one of the Spartans but is defeated by the Cheif by way (way?0 of a Shotgun to the face multiple times. They have defeated the remaining Covenant forces and Earth is safe. Even though it has taken quiete a beating mankind prevails once again and is saved because of the Master Cheif and the other Spartans.
So, I've run over your story and picked out most of the grammar mistakes and silly plot-holes.
In, my opinion, it's the worst rendition of a Halo 4. What are you thinking? This isn't the 'fall of mankind' if they end up winning, is it?
There's no indication as to how the Spartans escaped the Dyson Sphere, no mention of Halsey or Mendez who are probably the most significant characters in Onyx.
I know this is how you'd like to see it but you clearly know next to nothing of the Halo universe.