Good hair dye without using bleach?

Yesterday i dyed my hair with "splat" the color was aqua rush.it turned out more green.i don't want to and im not allowed to bleach my hair.it didn't cover all of my hair so im using the second bottle i got.is there any hair dye that's safe,last long,i don't have to use bleach on,looks good,and does not cost a lot of money?and my hair is kinda dark brown with Blonde highlights.