This video shows all of Viper's normal and hard trials in Street Fighter IV, with a camera angle that lets you see my hands, so you can see the timing for button presses and joystick movements. I use a MadCatz Tournament Edition FightStick. See some comments on specific trials below. Special thanks to guest cameramen Psyrell and Tbird!
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Normal Trial 3: Heavy kick to super is a bit weird. Probably best to press HK and then QCFx2 really fast during the animation, or else do one QCF, release, press HK + QCF+P. Careful you don't get forward+HK though.
Normal Trial 4: You get to have fun watching me fail on FADC, EX knuckle, ultra. Protip: it's infinitely easier (perhaps only possible) if you do a level 3 FA. For most of these combos that start with a FA, I've gotten into the habit of doing only level 2 to speed things up. I got a tip from the camera guy to start with level 3, and then I still sucked it up for a bit. Entertaining, though.
Hard Trial 1: This link isn't too bad, but canceling TK into super can be tricky if you're not used to it. I miss it a few times in this video, uncharacteristically (thinking about the later trials, maybe). You actually have quite a bit of time to see your TK come out, and then super, so no need to spazz your hands and hope it works.
Hard Trial 2: I recommend assigning a button to PPP here, just to make things easier (though it's obviously possible without). The motion you want after the focus attack is: cr.HP, QCB HP, QCF PPP, QCF PPP. Practice doing QCB, QCF, QCF kind of fast, and then you want to press one button at the end of each sequence (HP, PPP, PPP in that order). Of course, you only need to press PP after the first QCF, but PPP works, and with an assigned button, it's way easier to just press this. The QCB, QCF, QCF should all be about the same speed, and just press a button after each one. With a little practice, you can actually be really consistent with this.
Hard Trial 3: Perhaps Viper's toughest. Practice by high jump canceling (HJC from now on) a normal with a bit more stun (say, cr.MK or cr.HP) into ultra. The motion you want is: cr.HP, QCF, QCF + up-forward PPP. In numerical notation, it's cr.HP, 236, 2369 PPP. You have to press PPP just after the 9 input; you have to pick off the frames of Viper's high jump starting. Again, use a single button for PPP to make it easier. You'll probably get super coming out instead of ultra (because you can actually cancel super off these normals), but if that's the case, try moving your hand even higher (maybe to up) on your second QCF. The actual link combo itself is really easy. The HJC to ultra is the hard part.
Hard Trial 4: Much easier than 2 or 3. It's a fairly bread and butter Viper combo, actually, and one you should learn if you want to succeed with her. Unfortunately, the game wants you to do a GROUND burning kick (even though an air one works just as well for this combo), so the input for the trial is more strict. You have to HJC the EX seismo, and then do a burning kick before you leave the ground. The input for this is your standard "tiger knee" motion (2369 or 2368). Practice it outside of a combo for a while; the burning kick you get shouldn't look any different than a standard ground HK burning kick, but you should definitely be finishing on up, or up-forward. It's tricky, and unfortunate that the game makes you do it this way in the trials. In a real match, just HJC the seismo and do the burning kick in the air at your leisure, and the combo works just as well.
Hard Trial 5: A toughie, and learning to link two cr.HP like this is a skill expert Viper players will use fairly often. The input is cr.HP, QCB HP (in rapid succession)... [wait a bit], PP, P (in rapid succession). If you've been learning Fuerte's RSF combo, the input reminds me of that. The input + QCB move is fast, but then you wait a bit... then input PP and P very fast again. If you want to cancel a HP knuckle without it linking off a normal, you have to be VERY fast, but as soon as you cancel a normal into it, you have to wait a bit. If you're getting EX knuckle, you're hitting PP too fast (the game will take your PP input and override your HP input for the knuckle if you press them too close together)! You must WAIT until your HP knuckle comes out, then cancel it. Practice this on its own until you're somewhat confident in it. After that, it's more or less the same combo as Hard Trial 4 (again, you MUST tiger-knee the burning kick, because the game wants you to input a ground kick. In a real fight, you don't need to do this, an air BK will work just as well). Input the ultra almost as soon as you land; I'm pretty sure you don't need to worry too much about being early, but being late is a problem.
(less info)
As for making a vid showing how to "properly" use a stick, I might look into this in a month or so, when my schedule is more free. We'll see. I'm not sure I'm the best authority for it, but maybe I can give some helpful tips.
Dont got the money for an expensive arcade stick.