(I'm already booked to write a proper review of this game in a place that is not my blog. That'll come.)
I like to learn a character by just losing and losing and losing, which is why my Elizabeth has a horrendous record and is at 600 PSR (the ranked "how good are you?" metric: elite players are 800+). She is a very confusing and dangerous character to start out with, so I thought I would make some notes about playing this most moe of P4A characters.
The first thing you need to keep in mind is that this is an expert-level, high-risk, high-reward character. She has a lot of tools for offense at mid to long range, very little for defense, and a severely low 7000 HP. Liz gets hit by two big combos and she is dead. She is considered a low-tier character, but in P4A the tiers have one character at mega-good, half the cast at very good, and the other half at pretty good. SO IT'S NOT SUPER IMPORTANT.
With no HP and strong long-range weapons, you would think that she was a character like Nu or Lambda in Blazblue... but that's not exactly the case. Liz can pretty easily keep the opponent across the screen all day if she wants to with her huge Maziodyne beams (and against, say, Kanji she will want to), but at that rate she's chipping away the life bar for a small gain or merely stalling. It's something she's very good at, but it's not where her damage comes from. That's mid-range.
Let's talk about the beam. It's very useful, but it's not as good as it looks. It's predictable, it's very slow to recover, and if it's blocked at a reasonable range the opponent just gets the initiative to come in and attack.
You want to mix up your timing with this. Sometimes it's a good idea to hit them as they stand up with it. Sometimes it's not. When they try to dash in from a long distance, give them that beam. Mostly use the A, but mix in the B version when they're waiting around for you. They will start to jump up in anticipation, so mix that up too. Hop backwards and sometimes fire the beam in mid-air, or right as you land. You want your opponent not to know when or where the beam is coming, and ideally to be frustrated into running into it over and over again.
When the opponent starts to move in, that's what you have the B button for. Liz throws out one of her cards like a frisbee, and the move has extremely long range. At medium range, if the beam is blocked you're going to get hit. Not so with standing B. A hit with standing B is a combo starter, which usually leads to huge damage.
Go learn your combos. The AAA string has its uses, but auto combo isn't going to cut it, especially not with this character. You need the real ultimate combos to do real ultimate damage, which is the reason you're playing this character in the first place. Look the stuff up on Dustloop.
If B is blocked, then you can either try the sweep (also a combo starter with SB Garudyne) or start to go for the risky stuff with the Persona attacks from Thanatos. The standing C is a double sword slice. If this counter hits you have a combo with either the D throw or low C depending on distance. And it's gonna hurt like hell.
If you are blocked, you still have options. D makes Thanatos charge in with a slow throw that starts a combo. Low C is a slow move that pops out a bubble around Thanatos. A hit will put them into Fear mode, which increases your damage. It's an important move in all of Liz's combos and it's especially scary in the corner and as the opponent is recovering. After the first attack with C, you can also press C again for two more slashes.
Players will start to know to jump away from all this, because that's the situation you don't have a lot of answers for. After the initial strike with C, if you jump up and press C again, the Persona will also jump up and do its attack. You can often catch escaping opponents with this and slam them down.
The thing is, if they do just jump back and escape... it's time to keep them out with beams again. If they jump towards you, go for that low C.
Now when they're in on you is just a scary situation. You have the BD move, Shuffle Time, which is a very slow grab that walks (prances?) through attacks. The enemy gets a random status ailment when they're hit with the move; for your purposes the most useful are Charm (drains their SP, fills yours fast, crippling their offense), Poison, and good old Fear. Charm and Poison both lend themselves to just stalling the opponent at long range and hurting them in a small way.
But opponents are going to start seeing through this move (and your grab super) pretty fast. If they keep above you and just keep hopping, you're in trouble. When an opponent gets in on me I tend to jump back with A or B to range them out. If B hits there's a small combo there.
I find the grab super move is best used when the opponent is going through some predictable attack string that you're blocking: just find the gap in their attacks and pull them out of it. The range is longer than you think... but not as long as Kanji's throw range.
If you actually find yourself at advantage in a close-range situation, like after a knockdown, don't forget the old classics low jab and throw. If they aren't thinking about you playing the close range game, they might get tagged, and then you've got a combo. In the corner Liz's throw leads to deadly combo damage on counter.
To sum it up, Elizabeth has to make the opponent play her game. This is true in any fighting game, but controlling the rhythm of the fight is especially important for Liz because once your opponent gets their offense going, she has a hell of a bad time overturning that. And all the best characters in this game have amazing Shoryuken-style moves.. so it's going to be tough. Stay pushing, but be careful and don't go running headlong.