From what I remember you don't need to be online to get the Armor. I'll explain the whole process:
1. Start up the game and load "The Covenant" mission. If you have not beaten the game, you will not be able to go straight to this mission. Play through the rest of the game until you reach this mission. Play through the entire level until you get to the part where the Flood will assist you.
2. After the cinema scene where the Arbiter kills the Prophet of Truth, go back into the hallway where you entered. This hallway has a total of seven glowing rings.
3. Kill all the enemies in the room, and then go to the entrance, BUT DO NOT GO INTO THE EXIT.
4. Imagine that each of the rings in this hallway has a number. The one right in front of you is number 1, and the one right before the room with the Prophet of Truth is number 7.
5. Jump through the rings in this order: 4, 6, 5, 4, 5, 3 and 4. It is very important to jump through these rings only. Jump as cleanly as possible without touching the edges, landing squarely in front of each of them.
6. If you have done this correctly, all the rings will light up, and Music will begin to play, and the skull will appear at the end of the hallway either in front of the Hardlight bridge to the Platform that Truth was killed on, or actually on the Platform. If this does not occur, go back into the adjacent room and try again.
7. If the skull does appear, grab it. Now the last thing you have to do is carry the skull to the Exit, and jump into it.
And there you have it. Remember that you have to get ALL 13 skulls to get the Full set of Hayabusa Armor. The Katana, I've heard, will randomly appear once you've gotten 1000 gamerscore in Halo 3.