Extracting high quality image from a pdf to an image format

"I dont currently have adobe illustrator... Is there any other way I can extract the vector image in a high as quality as possible?"

LibreOffice Draw: https://www.libreoffice.org/

The best way is to use the Export All Images command in Acrobat. It will export the images in their original quality and format as stand-alone files.

Your image looks like it might be vector format, if it is, you will want to keep it vector for best quality. If you zoom way into the PDF, do the lines still look sharp? if so, it's probably vector. You have several options, you could simply use the PDF as a placed image, cropping unwanted areas. I would open the PDF in Illustrator* make my edits and remove any unwanted elements and adjust the Artboard (crop), then save as a new (Illustrator) PDF.

*Illustrator is not a universal PDF editor, but for this purpose, it should work well.

In Acrobat Pro, switch to the Edit PDF tools.

(If the panel doesn't appear on the right side of  your Acrobat window, you can open it from the main  Tools tab in the upper left of the window.)

1. A top tool bar will appear. Select Edit tool.
2. Click the graphic to select it, then right-click and select Edit With...
3. Then select the software program you want to use for this graphic, such as Photoshop. You can use any program on your computer.
4. Once the graphic is in the program, you can now save it and reuse it for your needs.

But keep in mind that this won't guarantee the quality of the graphic: it will only be at the original quality (or resolution) when the PDF was created. In other words, if the person who made the PDF made a low-res/low-quality graphic, then that's all you can get out of the PDF.