Corel's and Illustrator's coloring meshes are different. The problem is common when one wants to continue in CorelDraw with a drawing which is done in Illustrator.
An additional problem: If the mesh has a clipping mask in Illustrator, it vanishes when the file is opened in CorelDraw. Your image seems to use them.
The easy solution: Rasterize the problematic objects or the whole image in high resolution in Illustrator.
The hard way: Make in Illustrator so many ungroupings that you can reach the clipped meshes. Copy the clipping masks separately and reapply them in CorelDraw.
In Illustrator's Layers panel clipped meshes appear as groups, where you can see the clipping path as the top object.
After selecting all and applying ungroup 8 times in Illustrator the structure become this:
The only groups in the layers panel are the clipped meshes. Ungrouping does not release them, you must release the clipping masks. Do it and try to reapply the masks in CorelDraw. I couldn't try it because my CD is from the stone age.