How do I get rid of this unwanted bar from Eclipse?

The bar you are talking about is the breadcrumbs.

To remove it, look at your toolbar which should more or less look like this:

Then, click that button that is on the very far right. It looks like a little C with a green circle, a black triangle, and some small blue thing in the back. Find that button on your eclipse toolbar and click it to show/hide breadcrumbs.

If you don't see it, let me know, and I can try to figure out which toolbar it is a part of.

Using the Scala View, I neither had the icon mentioned in the accepted answer nor did Alt+Shift+B work.

What did work for me: Right click in the unwanted breadcrumb bar and click Hide Breadcrumb.