...without losing some of the image.
Not sure what you mean by that. Your best bet would be to open the image in Photoshop and resize/crop it there to your A4 page (+bleed) at the desired resolution. Then Place in InDesign, and no resizing should be needed.
OR, resize in InDesign using a corner handle while holding down Ctrl/Cmd+Shift. If the image is much larger than needed, this will push the effective resolution (see Info panel) up, and potentially cause a processing-bloat problem at output.