trouble with removing a background from an image

Re-reading your post, I may have misunderstood what you are aiming to do.

You traced the image. Make sure that the pen path is on top of the fish image.

Select both the pen path and the fish image. Then choose Object > Clipping Mask > Make.

My suggestions are for Illustrator because this is the Illustrator forum. However, Met1's suggestion would work great in Photoshop and would take less time.

Barbara's answer is the Illy way. Got photoshop? It's one click and done there (okay, not quite - rename your layer (just so that you can have a transparent background [double click layer, enter]), use the Magic Wand Tool on the black (tolerance of 16 should be fine), delete, save as.)

I'm not sure what you mean by "lift it out of the background." If you have traced the image with the Pen tool, you should be able to delete the image when done so that only your traced objects are visible.

In the Properties panel, there is an Image Trace command that could work for you. After using Image Trace, you can click on Expand in the Properties panel. All of the objects will be grouped. You can then use the Direct Selection tool to select and delete the black areas.

After image trace using the High Fidelity Photo setting: