When little eddie is out he wants to loop you, where he uses overheads and stuff to get you into a combo, if that fails and little eddie is about to dissappear he will most likely attempt a grab. Or in some cases attempt a grab earlier. There's three options:
1. FD big eddie and normal guard little eddie.
2. IG little eddie and normal guard big eddie.
3. FD big eddie and IG little eddie.
All 3 options push you away from big eddie, that way he can't throw you and can only keep up the pressure till little eddie runs out. And with this if he attempt an unblockable you can jump defend.
From here on I consider the lamest behaviour, rather then taking it like a man, some eddies want to run away and wait for little eddie to refill. This WILL mean you'll be receiving drills and FB drills. The best way to get over that is by runjump FDing till you get near eddie. Once you're close and see an opening and Eddie is a bit careless you have a free CH j.H into combo. Even if he's not careless you can setup your offense from that spot and he wont be able to escape until little eddie shows up again.
As for the Testament match up, I've played it myself. It's a fucking pain in the ass, have a nice day. Anyways, it still depends on the testament you're playing. If the Testament you're playing tends to attack you, or better put is aggresive he's fun to play against. But you probably won't have to expect seeing such a Testament often, if at all.
Since Testament flourishes at zoning, he'll be at the other side of the screen with his traps out exe-beasting before you even had the chance to say "Aaah". Now someone at the other end of the screen isn't a problem, the fact that there's a gazillion amount of garbage in your way is what makes it hell. The best way to get in is using jumps to get over the trees and punches to get rid of the web. God forbid, don't try j.H on a web, cuz you'll get stuck 99/100 times and Testament has a free combo on you. Also, while jumping, don't accidentally land on a tree, because Testament will miraculously wake up out of his keep away game and attempt to attack you, since his overhead low game is pretty good, you'll most likely eat hits.
Once you actually got to a corner, he's supposed to be stuck... Until he decides... yes you guessed it, if he gets a remote chance he'll reversal your ass with his catch moves, you'll be poisoned, eating a combo, have that fucking rave on your ass and if you FINALLY manage to get out of his attack, you're back at square 1, except you actually lost health rather then did damage to him. So when you get up close you MUST NEVER EVER fuck up.
Now that we're on about keep away, Faust is the same type, with the damn garbage as well. You go about this like the testament match up, the catch here is however, you'll be most likely to stuff anything Faust tries on you to keep you away. By doing so you get the CH j.H into a free combo and you'd make faust more careful. When this happens you can proceed to a normal rush down without the worries of being catched and reversaled.
Going up against Baiken, do mind the tatamis, don't be a fool and get CH'd by them. Just blocking the tatamis while running after Baiken already gives you a 50% higher chance of beating her. So now the other 50%... She likes to reversal, she could swear by it! So if your opponent is reversal happy, you're gonna P and then delay. Now what happens here is that the blockstun is too low for a human to reversal it, so Baiken will do an ordinary low. This is the moment where you CH sweep, charge and continue with your combo. Once your opponent has become more careful, don't get all cocky and launch full blockstrings on her, because you'll still eat a reversal. Minding the above, you can continue with a normal rushdown game once up close and destroy her.
There isn't a lot to say about Jam, other then she does abnormally high damage off of random hits. To avoid these random hits or get a trade at worst, you could use l1Ri. Also note that Jam most likely will not attempt to rush you down but rather wait you out. It's very important that you remain solid even if your opponent is attempting to get the worst out of you.
Venom and Axl are kinda like Faust, but with aimed garbage. Venom needs time to set up his balls, so this will be the time you won't be giving him. Axl really doesn't like the risk of you up close, so getting in will most likely be a bigger problem then actually dealing with him once you're in range. With both of them, original jumping patterns are key to getting close. And if they do stupid predictable shit, punish them for it, that's what OS is for.
Against Sol: do not get predictable, this is a rule of fist against anyone, but it counts even heavier against Sol. From there on you should try to jump, doublejump his GF. You should NOT use gun blaze at random against Sol, he has too many tools to stop it(unless he's a dumbass, then you can GB away to your heart's content). If you're able however, you could GB any BB attempt unless there's a GF covering it.
Potemkin: you have the priority, he pretty much has the damage. Since your character favors PB ranges... you're fucked. If he wants to go for okizime games, SV is a nice tool, otherwise you can also mash backdash which should help you stay clear from slidehead and airgrab loops. If Potemkin goes for an air attack OS gets a free gun blaze. This also applies in response to follow ups ending with storm viper. So whenever you land with OS and Potemkin still has to land, be sure that he has to block a flame before he gets on the ground.
Against Zappa: BE FUCKING PATIENT. The very moment he fucks up however, don't hesitate to FB him for free damage. Keep in mind he has LOW PROFILE written all over him, this renders your Ri and GB useless, since BRP is slow on start up, you can't use that on reaction either. To win you need solid play. By all means: don't catch unnecessary shit like ghosts. Kekken and I have tested, Zappa's dog unblockable cannot be slashbacked, so don't even bother.
Robo-Ky: I've played this match up quite a bit, it's pretty straight forward. Don't do stupid shit and you're fine. The best part however is when he sets his time bomb. What you should try is to interrupt him before that super discharges, the moment it does you need to be out of range, doing that successfully means you can charge to lvl3 for free while he's discharging and damaging himself.
Against Chipp: If he likes to alphablade in air from across the screen, FD and punish it. From there on the match is pretty straight forward.