Convert JPG Artwork to Vector

I have a single JPG graphic that must be redrawn as a clean, fully scalable vector. The final artwork needs to look identical to the original—same colours, shapes, and proportions—but with smooth, closed paths so it can be printed on large banners or used as a tiny icon without losing quality... (Budget: $2 - $8 AUD, Jobs: Adobe Creative Cloud, Adobe Illustrator, Adobe Photoshop, Digital Art, Graphic Design, Illustrator, Logo Design, Photoshop, SVG, Vector Design)