I have a four year old, not adopted, but he sometimes has mega-tantrums, especially when there are other things going on for him and he definitely had them at 2 - I haven't changed much in how I deal with them aside from the fact that he is now physically stronger so there are changes I've had to make from that POV.
I find that the best approach is to get down to their level, herd them (or carry if necessary) to a safe place, away from the setting where the tantrum was - so if upstairs you could take her to the sofa, if downstairs taking her to her room might help. Not as a punishment, just as a place to sit down and chill out.
Sometimes just changing the setting is enough to break the tension and they will talk calmly, sometimes it requires more, but the fact you've taken them away from the scene of the original upset helps. If you can contain them in that one room/area then that's useful too (I mean by blocking their exit etc, not locking them in on their own!)
You must ignore everything that they say even if you find it hurtful because they are just lashing out. Don't be tempted to respond to it other than with something reassuring like "Well, I love you." or "Okay." or "That's okay." If they're lashing out physically then don't sit there and take being attacked, but try and stop it in a gentle way by e.g. holding up your own hand to block their hitting, or holding their wrists to stop scratching, pinching, grabbing. You can hold them facing away from you to stop biting and kicking - they can be strong though at 4+! If you have anything like a stairgate they can't get over then you might have to resort to putting them behind that if they are being physically violent and you cannot prevent it, but generally being there and being present even when they're being horrendous is important if you can possibly do it. I have put DS in his room before and closed the door when he's chucking stuff at me because I've felt I had no choice but I've kept on speaking to him through the door in a calm voice saying "I can't come in when you're throwing things. That hurts me. When you calm down I can come in." etc.
Tends to wind my 4 year old up, but if your DD is emotionally at the level of 2 she might respond to this - if you give her a name for the feeling or encourage her to show you how angry etc she is - you could get something like some beanbags and ask her to throw them at the wall and say "Show me how angry you feel! Throw this as hard as you feel angry!" and then when she throws it you can say something like "Wow, you feel REALLY angry about that." It's just about getting her to talk about her feelings and realise that they are okay to have and that they don't have to be a scary overwhelming thing. Some children also respond really well to being asked to draw you a picture of how they're feeling. You could do this when she's feeling calm and happy too, just ask her to draw a picture or describe how she feels when she has certain emotions, join in the conversation yourself, like a PP said you could describe feeling anxious as having a funny feeling in your tummy, and feeling sad like feeling heavy and like there's something stuck to your chest and how anger can feel like boiling water bubbles inside you and sometimes it spills out.
It's really common for upset over unrelated things to spill out over minor issues like losing control of a situation (being asked to do something they don't want to do and not being able to refuse/not knowing how to communicate she doesn't want to) or something happening not as she was expecting, so try not to take it personally when she does flip out over something you've said or done - remember it's not about that, really. Also, if she says things like "I hate you" or "I want to go somewhere else and never ever come back" - the kinds of things which sound terrible to us! - it's more likely that at that moment in time she's not feeling particularly favourable towards you, but it's coming out as "I hate this forever" - that's an age thing as well as a tantrum-related thing, because at her age it's very difficult for her to imagine how she might feel at some given point in the future. Just like when toddlers/preschoolers are having fun, they say things like "I love this. This is my favourite thing in the whole world. X is my best friend. I want to stay here forever and ever." when actually what they mean is "I'm really enjoying this right now" - next week they'll probably have a different best friend, refuse their "favourite" food and get bored quickly of the place they loved before. They're fickle but they don't know it!
And then my only other tip is to make sure at all times she has enough food and enough sleep, and if either is lacking, expect tantrums. If you can at all avoid it try to steer well clear of the hungry/tired hell cycle when they become too tired to eat properly because then it's hell on earth to try to get them to do anything, they're too wired to sleep, they won't eat without creating a huge scene... aargh! But if it does happen be prepared and just keep repeating the mantra... this too shall pass, this too shall pass!
