My car will shift good out of 1st unless I hard accelerate from a stop it will have an extended shift. This is a normal occurrence when doing into 3rd and 4th. It will start the shift and all you hear is vroommmmmm until it will finish the shift. Can someone tell me what I am looking at to fix the problem?

Try changing the transmission fluid with Mobil 1 Synthetic ATF. If that does not improve the situation, you are likely looking at a rebuild. Change the fluid while it's hot, for a fast complete drain. Easy job.