And educate yourself about tattoos. People think that simple tattoos are easy. Actually, it's just the opposite. There's no where to hide in a simple tattoo. Thin lines on thin skin are prone to blow out. Learn how to tell a good artist from a hack.
It looks pretty rough and full of blowouts. I think you need someone to cover that up and just put the dainty bird somewhere else. Also, don't go back to whoever did that. Find a new artist who excels at coverups.
"Dainty" usually involves thin lines. There might be an artist out there who incorporates both dainty and thick into the same images, but that's not what I usually look for - so I'm not familiar with any.