Blink and Mirror Images is a very powerful combination against martial characters, you really had little that you could do in that situation. Fighting against such enemies requires planning and preparation. The only thing that you and your group could have done, without having prepared against this, is to have a blanket Dispel Magic ready to remove his buffs.
However, get a Truthful weapon if possible. A +1 Truthful Dagger (+3 total) should always be available from now on, or you risk finding yourself in a similar situation again when fighting outsiders and BBEG's again.
A truthful weapon unerringly pierces concealment provided by illusions, allowing the wielder to ignore the miss chance provided by illusions such as blur, displacement, and invisibility. Attacks with a truthful weapon against a creature affected by mirror image or a similar figment always attack the real target.
True Strike actually only works against concealment, it doesn't allow you to pierce illusions or the miss chance of ethereal creatures. But it does help against Blur, another common spell used in combination with Mirror Images.
And Dimensional Anchor (or a Phase Lock weapon) really doesn't help, unless you are really lucky and don't hit one of the images by accident. You would need to already be ignoring the spells's effects before anchoring the target.
Closing your eyes
Due to how concealment and miss chances work, (RAI) you should never have more than 50% chance to miss a target, as pointed out by James Jacobs (Creative Director). So granting yourself blindness or a similar condition could help you against Mirror Images, while still maintaining the same miss chance.
However, there are no hard rules about how this works. We don't know if this is a free action, how long it lasts, if you can close your eyes before attacking, attack, then open again. Many community members are Paizo believe this is cheap, and a common house rule is to allow you to close your eyes, and accept the benefits (gaze attacks) and penalties that come with it (blindless) until the start of your next turn.
A (ex) developer commented on this, suggesting to spend a Move Action so you close your eyes and focus that the images are not really there, or your brain will still try to target one of the images because he couldn't really tell which one was real before closing his eyes. And this makes some sense, as you normally would need to spend a move action to accurately perceive the location of an invisible creature.
Bring a shotgun to the fight
No, seriously. I know that some GM's don't allow firearms in their games. But if you do, the Scatter quality of shotguns is not affected by the miss chance of Mirror Images or the concealment granted by Blur (should that situation arise in the future). This has been confirmed by Stephen Radney-MacFarland (designer):
Effects like the mirror image spell, or effects that grant concealment, such as smoke, fog, or the blur or invisibility spells, do not foil a scatter shot attack.
Similarly, effects that affect an area should always help against Mirror Images. However, the miss chance from Blink is still there.