Both blink and displacement give my opponent a chance to completely evade my attacks (regardless of my attack roll) and prevent me from ever dealing sneak attack damage.
From 3.5e, I know that true sight (range: personal) and dimensional anchor (needs to hit first) are the correct replies, but our party is a little bit lacking in the spell department.
Is there any feat, mythic boon, or piece of equipment I can get myself to deal with this issue?
I'm playing a level 10 unchained rogue with the hidden blade archetype (granting me Path of War maneuvers from the Broken Blade, Mithral Current, Thrashing Dragon and Veiled Moon schools) in a mythic campaign (currently mythic 2).
Last game we faced a single level 9 wizard with displacement and mirror image and we only manage to hit her once or twice in the fourth round of combat, right before (having consumed all of her spell slots) she teleported away to safety after dealing tremendous damage.
Note: Much later, I realized that, as an unchained rogue, partial concealment is not enough to prevent my sneak attacks. The question is still good since it also focuses on completely missing the opponent, but just so you know… it's a bit less bad than it used to be.
Best Answer
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.
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):
Similarly, effects that affect an area should always help against Mirror Images. However, the miss chance from Blink is still there.