I would rule that a 4th level spell trumps a second level spell. Close your eyes, and use Blindsight and the images are not a problem.
Yes, you close you eyes and use your blindsight to attack them, thus negating Mirror Image.
In the RAW there's nothing that specifies that this work to counter act it that I see, neither in the Blindsight rules or in the Mirror Image rules. That said, it can definitely be inferred easily. Mirror Image say that you must be able to see the images for them to effect you. Closing your eyes or similar tactics can negate it, thus, using Blindsight with your eyes closed will render you unable to see the mirror images, and immune to its effects, but able to attack normally.
Note that this is specific to Blindsight, not Blindsense. Blindsense could still tell you which square is attacking you, but specifies that its not specific enough to fight by accurately, so closing your eyes when you have Blindsense will still incur the normal penalties for fighting blind.
So basically, nothing specifically says it works, but you'd be hard pressed to find a GM who doesn't buy the argument that it does.
You would not even need to close your eyes - your blindsight would tell you which image is real every time. I could see someone closing their eyes for flavor though - it's easy to imagine the additional images as confusing. You don't have to be blind to use blindsight or blindsense (e.g. Dragons, Bats).
We play tremorsense bypasses it too
Tremorsense appears to work (on creatures touching contact with the ground) like blindsense, not like blindsight. So you know what square they're in but nothing more detailed than that, which isn't enough to overcome mirror image. See Eidolon tremorsense ability.