Help with toddler attacking older sister

Any help or advice would be greatly appreciated! I have 3 children, 6 year old son and 2 daughters aged 4 and 21 months. Over the past 2 months my youngest daughters behaviour has gotten appallingly worse with her older sister! She pulls her hair so much that she actually pulls chunks out, she nips and just generally attacks her, my oldest daughter does not in any way provoke it! We have tried time outs, taps on the hand, and getting my oldest daughter to pull her hair back to show her that it hurts, she just goes straight back to attacking her 5 minutes later. She does not do this to our son or anyone else! I am at my wits end as it can happen anywhere, in the shops at the park ANYWHERE xx