It sounds like she doesn't trust you at all and clearly does not want to be touched.
Unfortunately, making a budgie be "tame" by forcing it to be held does not perpetuate tameness at all, and in fact, encourages a master/servant relationship based on submission.
She's scared right now, and afraid you will hurt her whenever you pick her up and force her to be touched. Lucy is a sweet little budgie at heart, but the way she perceives you causes her to bite.
She's biting because she's trying to defend herself, and even though now because of this it will take longer to tame her properly, it still can be done!
Because of her aggression towards you, she may start to take it out on her cage mates, which isn't a good situation, either. If possible, try to move her into her own cage, separate from the others. Three budgies may bicker if caged together anyways, so this may be for the better.
Here is a quote from FaeryBee on the best way to tame budgies:
Originally Posted by FaeryBee
Taming and Bonding is all about helping your budgie learn to trust you and it takes a great deal of time and patience on your part.
You should never grab your budgie or force her to be touched.
Most budgies once they pass the "baby" stage, do not like to be petted or touched.
If your budgie does like to be petted, you should only ever pet her head, neck or chest area.
Stroking a budgie's back and/or tail stimulates its breeding instinct. Bonding means allowing them to choose to be with you.
To bond with your budgie, you need to build her trust in you.
She will have to learn over time that you will not hurt her, grab her and try to force him to allow you to hold her.
To build your budgie’s trust, sit by her cage and read, talk or sing quietly to him for a period of at least 10-15 minutes, 3 or 4 times day. After the 2nd or 3rd day, rest your hand on the outside of the cage when you talk to her so she'll learn that your hand is safe and will not hurt her.
After a week, rest your hand inside the cage when you talk.
Don’t make sudden moves, don’t try to touch her.
Let her get used to the idea that the hand is now in his safe place and not harming her. If she becomes agitated, stop moving your hand and just hold very still until she calms down.
After 2 weeks, begin moving your hand slowly toward your budgie. If she becomes agitated, stop moving your hand and just hold very still until she calms down. When she's comfortable with your hand near her, you can offer her a bit of millet or a few seeds. In a few more days, you can begin your taming and bonding sessions.
Always work at your budgie's pace.
Move slowly and talk reassuringly and calmly to her whenever you interact with her.
Remember, patience is your friend. If you're doing everything right and she still bites you initially, set her down in her cage, say "No!" firmly, and exit the room. Wait a few minutes so she knows you left because she bit you. Budgies are very flock oriented so rejection from their flock for their behaviour generally is a good cue to them. Don't try to "discipline" her in other ways, budgies don't understand yelling. My girl bites sometimes when she's moulting and crabby, I do this and she's gotten better about it over time.
Best of luck and please be sure to let us know how starting from the beginning goes!