Do you mean the link to the topic isn't working? If that's the case, this link should work properly:
http://forum.speeddemosarchive.com/post/metal_combat__falcons_revenge_speedrun.html
Are you at Thanatos or Virvius right now? I'm guessing Thanatos, since that makes the most sense, but I don't want to assume, especially because it does make a difference.
As for videos, I don't know that I actually had one of a Thanatos battle with the Tornado. I can tell you what my strategy was and hopefully it might help you come up with one for hard mode.
The key to my strategy was to go for his shoulders. Pattern luck was also necessary. I need him to give me enough time to charge a level 5 shot. Usually this requires him to go offscreen, but not always. When he rears up for a charged shot, I peg him in the shoulder and quickly follow up with a bomb to delay him. This allows me to charge up another level 5 shot and peg him in the other shoulder. I immediately follow up with another bomb, but aim it right at his head, so I do damage to both of his shoulders. This actually destroys them both at the same time causing massive damage and a level 3 shot is enough to finish him off.
My time was 9"45. I'll run a test and see if it's possible to do this on hard mode. I can also dig out the video, as well.
And back to enemy behavior, yes. Actually, there are several factors I have noticed. Where your charge bar is at can make a difference in what your opponent does, as well as each shot you fire and how strong a shot you fired. Bombs also can cause pattern changes. I think Arachnus is the most reactive to everything action you take. One thing that may or may not matter for Giga-Desp 1, in normal mode, he will expose his weak point a lot sooner if your charge bar is empty. I'm not sure how it works in hard mode, but that may be something you should watch out for.
One last thing, if you aren't already aware of it, there's a glitch for a fast kill of Arachnus with the Tornado. I haven't yet been able to get it to work on hard mode, though, so I don't know if it will work. I'll give that a few more tries and let you know how it works out.
EDIT: I verified that at my Thanatos strategy on normal will work in Hard. With some reloading and frame advance I was able to get a 9"25 on Thanatos. Here's a video of that Thanatos strategy:
http://www.youtube.com/watch?v=Mg59jTK48Zg
The Arachnus glitch will also work. Here's a video of me pulling it off in normal:
http://www.youtube.com/watch?v=pLQQPn59rQM
Apologies for the video quality on both, hopefully you can make out enough to know what's going on.
Now regarding the Arachnus glitch, what I've found needs to happen for this to work is that there have to be a lot of objects on screen at once. Asteroid explosions work really well for this. Also, the charge bar needs to be at least 7 for it to work. For hard mode, the real challenge will be not only be getting Arachnus to have a favorable pattern, have him travel through a field of asteroids, and have him destroying them as your charge meter is at the right level all while making sure it happens fast enough to be worth doing.
But if you can pull it off, it's a great trick to use. Even more so because it's on an opponent halfway through the game.