@cRAZYtALK: Breeding the Hidden Power the traditional method (mass hatching eggs) takes a very long time (like probably a week or more IF you have parents with 3 correct IVs each), and to have even more restrictions (i.e. mixed attacking IVs) will pretty much triple that time ... assuming you want decent special attack and speed. The ideal IVs for Hidden Power Ice are:
31/30/30/31/31/31 or 30/31/30/31/31/31
You probably want to have 31 Speed IV. If you don't care too much about the other IVs other than attack, then you need to have:
EVEN number for Defense IV
ODD number for Special Attack and Special Defense.
To get at least 65 Base Power for your Hidden Power, your Special Attack, Special Defense, and Speed IVs, when divided by 2 and then rounded down, should be ODD (i.e. 31 / 2 = 15.5 = 15 = odd, and 30 / 2 = 15 = odd).
If you really want to keep Attack at 31 and do not want to learn how to RNG (which is probably the faster way to do all this since learning takes a few hours max and you can capture a HP Ice flawless naive Mienfoo in less than half an hour), I would suggest trying to breed until both of your parents have 3 good IVs. In this case, 31 in attack, special attack, and speed seems ok (usually you should try for SpA, SpD, and Speed to ensure Base Power is at least 65).
With the correct Attack, SpA, and Speed IVs, even if you get Hidden Power Ice, you will only be guaranteed that it is 46 Base Power though (Special Defense counts for A LOT in determining Base Power). In comparison, if you have 31 Attack, SpA, and Speed and your SpD is odd and SpD divided by 2 rounded down is also odd, then your base power will be guaranteed to be at least 66.
I'm not sure why I went about explaining so much, but basically you should probably learn how to RNG if you want to breed for Hidden Power. You should still need to know how IVs determine Hidden Power type, so I recommend reading a guide like this one:
http://www.smogon.com/ingame/guides/breeding_guide_part4 (Read it a few times while testing things out if you don't get it).
To learn about how to RNG for your pokemon, go to the Wifi forum and click on one of the stickies about RNGing.
If you "cannot" learn how to RNG and must then breed it the traditional way, here are the steps you should take. Now here I am going to assume that you want HP Ice more than you want 31 Attack IV, so here are the steps to get Hidden Power Ice first:
1. (Beginning Phase) Find a Mienfoo that has as close to x/x/30/31/31/31 as you can, most emphasis on the last 3 IVs. If you have nothing, then just catch a few random Mienfoos or breed for them until you have at least one of those IVs. If you have a male pokemon breedable with Mienfoo that has one of those IVs (i.e. 31 in SpA/SpD/Speed), then of course you can attach the appropriate Power Item and breed with Mienfoo too.
2. (Replacing Parent Phase) Keep note of the breeding parents' IVs (mainly just which ones are 31s, or 30 for Defense). When you have a male hatched Mienfoo whose IVs are better than the IVs of the current male parent, then replace the male parent with your current one. Same for female. If you have a female naive, then sure, attach everstone. Male parent should hold appropriate Power Item too.
3. Repeat Step 2 until you have both parents having x/x/x/31/31/31 or better with female being naive holding everstone and male holding Power Lens/Band/Anklet. With those parent IVs, you now have a 1 in 16 chance in getting a Hidden Power Ice pokemon with base power of 65+ (actually higher chance than 1/16 with Power Item). Keep at it and you will eventually get a x/31/x/31/31/31 pokemon with HP Ice 66+.
EDIT: (Assuming you have no other means of calculating IVs) It helps to have about 30+ Rare Candies in storage so you can save before checking IVs, and then rare candy up while putting stats in an online IV Calculator (don't tell me you can't find one). Alternatively, another slightly faster way is, after the initlal phase, when you know for sure that you have at least one flawless IV, you can go to the person in Nimbasa City inside the Subway. Talk to the first person you see when you do down those stairs and he will tell you what your pokemon's best stats are. If he says your pokemon is amazing (or whatever he says) in more than one stat, then you know that your pokemon has at least 2 flawless. This is OK for when breeding for HP Ice since you want 31 in SpA, SpD, and Speed anyway. For other Hidden Powers where you want some 30s mixed with 31s this way won't work so well.\
EDIT2: I forgot to mention (though it is sort of implied). I would not recommend holding Power Bracer throughout this whole process, because retaining 31 Attack stat will only delay your process of getting those good HP Ice IVs. It's much faster to get those HP Ice IVs first for SpA/SpD/Speed, and then just chance your 31 in Attack. *Much Faster* meaning it'll maybe take a few hundred eggs instead of a thousand or something like that if you are lucky.