Looking at both this question about how faerie fire interacts with mirror image and this question about whether you can target the illusory duplicates themselves, I saw that both quote this section of mirror image:
A duplicate can be destroyed only by an attack that hits it. It ignores all other damage and effects.
I am now unsure how to interpret this with regards to dispel magic, which I would certainly argue destroys the illusory duplicates and would consider it to be an effect.
Dispel Magic works by targeting:
Choose one creature, object, or magical effect within range. Any spell of 3rd level or lower on the target ends.
You can target the effect, mirror image, or you can target the creature that has it. The specific rules around dispel magic allow for targeting of a spell effect when normally you don't (such as the general rules around mirror image.)
Most importantly here, you're not 'targeting' a duplicate, you are targeting the spell effect. That's any spell effect, it just happens to be the spell effect of mirror image.
Either way, the spell is dispelled.
I think you're being confused by the difference between the images being destroyed, and the spell ending. Dispel Magic doesn't destroy the images, it ends the spell/effect. Similarly, Mirror Image has a duration of 1 Minute. After this one minute, the spell ends, and the images wink out of existence, regardless of whether or not they were attacked.
On another note, entering the area of an Antimagic Field will suppress the images, but they will wink back into existence upon leaving the area.
Dispel Magic is a spell that can be used targeting a creature, requiring no attack roll:
Choose one creature, object, or magical effect within range. Any spell of 3rd level or lower on the target ends.
Mirror Image does not stop spells that directly target a creature with no attack roll (see this Q/A). This means that such a spell affects a creature normally.
Therefore, you simply target the creature and the Mirror Image spell ends, (causing the duplicates to vanish because the spell ended). The fact that duplicates "ignores all other damage and effects." does not matter because by using Dispel Magic on the creature you are ending the spell itself, not a duplicate.
Dispel Magic can either target "one creature, object, or magical effect." If Dispel Magic targets the creature on which Mirror Image was cast, it doesn't destroy the duplicate, it ends the spell maintaining the duplicate (causing the duplicate to end). The clause in Mirror Image can't apply unless Dispel Magic specifically targets the duplicate. As the former is the more intuitive way to use Dispel Magic in this situation, the latter, more complicated case can be ignored.
Be careful of the answers that imply Dispel Magic does anything other than end a spells duration. I think that is important to notice that Dispel Magic is a non-line-of-sight targeted spell. Mirror Image creates duplicates for 1 minute, that last the duration or till they take damage. Your target is the Mirror Image spell, not one of the duplicates.
Dispel Magic works by reducing the remaining duration of the spell to 0, causing the spell to end just like if the duration normally expired. (So levitate would still do the gentle fall if it's dispelled)
Since Mirror Image duplicates do not persist after the spell ends, the duplicates disappear. THAT is why Dispel Magic works (not because Dispel Magic can "destroy magic on a creature", but because it does exactly as it says. It ends a spell (reduces duration to 0)
