Why a witch? The spell list is poorly suited to buffing your attacks and the hexes are largely unrelated to archery. Sure, cloak of winds is a nice spell, but you don't have to be a witch to get it.
Edit: I misremembered. Witches don't get cloak of winds ... so you don't get nice defensive spells either. You're missing out on this, mirror image, divine power is an age away and you don't get haste or similar beforehand. I don;t see the reason for this combination of role and classes.
Some questions:
— Any reason you're plugging Eldritch Knight instead of Arcane Archer? Generally speaking, the benefits of arcane archer outweigh stacking your fighter level via Eldritch Knight levels.
— I'm not sure why you're trying to build towards here. It looks like you're trying to essentially be a bard: decent at fighting, some debuff spells and healing. Overall, its not a bad build. In fact, I sort of like it (though I'd like it better with Arcane Archer). What hexes are you planning on taking? One of the witch's weaknesses is that her hexes don't scale when she multiclasses.
— It looks like you're taking the Strength patron specifically for Divine Power. I don't think I would do that, personally. Many of the other spells (such as Righteous Might) are worthless to an archer. That said, I see the benefit of having a quick attack roll boost: I just don't think its worth it because you don't have many spells per day.
— The 8th level Hedge Witch ability doesn't look all that great to me, but that's just my opinion I guess.
Here's what I would do:
— Witch 5 / Fighter 1. Get into Eldritch Knight at 6th level.
— Witch 5 / Fighter 1 / Eldritch Knight 3. Get into Arcane Archer at 10th level.
— Witch 5 / Fighter 1 / Eldritch Knight 3 / Arcane Archer 4. Go back to Eldritch Knight at 13th level.
— Witch 5 / Fighter 1 / Eldritch Knight 10 / Arcane Archer 4.
This accomplishes several things.
— Arcane Archer's seeker arrow ability is really great. Its arguably better than Improved Precise Shot, even if it has limited daily use.
— Arcane Archer's imbue arrow is even better: if you use a longbow, then you can modify any area spell to use your bow's range. There are plenty of nasty tricks you can do with this ability, most of which involve black tentacles.
— You cast spells as a 17th level witch and have a base attack bonus of +17. This means that you get 9th level spells (abet one per day) and still boast a wicked attack bonus; better than a cleric, actually.
Now, if I were you, I would focus my hexes on options that don't care about my witch level. Cauldron (Brew Potion as a feat for free) is a good example. Prestige Classes don't stack themselves with your witch level for improving your hexes OR your Patron Spells. That's right, you don't gain any patron spells beyond those earned at 5th level in this build.
Cackle+Vital strike=Win
[quote=]Prerequisites: Base attack bonus +6.
Benefit: When you use the attack action, you can make one attack at your highest base attack bonus that deals additional damage. Roll the weapon’s damage dice for the attack twice and add the results together before adding bonuses from Strength, weapon abilities (such as flaming), precision-based damage, and other damage bonuses. These extra weapon damage dice are not multiplied on a critical hit, but are added to the total.
Cackle simply extends your effects, and is a move action
So you can combine the two, debuff enemies and deal decent single target damage.
Evil eye + cackle + vital strike sounds like an interesting idea.
When going standard witch focused shot can be as good as, or even better than, vital strike. Instead of rolling twice you add your int bonus to damage. I don't know if it works but it might be interesting to look at kirin style, too.
Dustyboy is right about cackle. Because cackling is a move action, you could effectively spend your first round of combat setting up a debuffing hex (Evil Eye is best because I don't think its penalties improve with level) and then for all subsequent rounds, you can spend one action to increase the duration and a second to attack for double damage with vital strike.
As a matter of fact, your Base Attack Bonus would be good enough that you could take Greater Vital Strike at 19th level, when you earn your final feat.
Between Greater Vital Strike, Weapon Specialization (which you said you wanted), and Greater Weapon Specialization (which you could qualify for if you saved your arcane archer levels for the final four levels of your career instead of taking my advice), you'd be rolling 4d10 damage + 16 (Deadly Aim) + 1 (Point Blank Shot) + 4 (Weapon Specialization and Greater Weapon Specialization) + 6 (Devastating Strike) + a free d6 from your choice of shocking, flaming, or frost a la arcane archer. That's an average of about 45 damage, with a maximum of 73 damage.
Is it great? Not really. Vital Strike is best when you A) have a low attack bonus or B) have a good source of extra damage like sneak attack. But its still an option, and not a bad one at that. 45 damage + extending your debuffs is pretty cool.
If you worship Erastil, Savior's Arrow could be a fun feat for you.
Its from Inner Sea Gods and it allows you to shoot your allies with a cure wounds spell once per day. You effectively use your longbow's range for the cure spell instead of "touched creature."
Its once per day, but good for an emergency snipe heal on someone far from you.
If you particularly dislike wizards and you want to heal then I'd go with a cleric. Maybe Cleric 8 / Holy Vindicator 10 / Cleric +2. Choose a deity with longbow as the favored weapon (in Golarion, Erastil; probably Feather and Growth sub domains). Later on you might get the Channel Smite and Guided Hand feats to reduce the number of attributes you need to get stat boosters for, but initially you'll need the feats for archery.
You don't lose caster levels until after you get the good archery buffs, your BAB at 20 is +18, you can wear armour, as a cleric all the healing spells are yours, you can fly using your own spells, and you get a pet to hold off people trying to melee you.
Witches spells just aren't as good at buffing as their competition.
I might also point out that a composite longbow, in conjunction with gravity bow.... and The Orc witch doctor archetype (Con casting)You will wind up as a dex/con character with a higher than average str, throwing in the Mother's teeth trait (Or if your DM allows it, toothy) will give you the ability to actually deal with enemies at a closer range for those tight spots.
Charisma,Wisdom, and Int can safely be dumped.
Most simply take less levels in holy vindicator; cleric 8 / holy vindicator 4 / cleric +8 gets you +16 BAB by 20 if barely and leaves you with a level 17 companion at 20 assuming boon companion. I'd thought of the AC as a low level trick but you can keep it going if desired.
If you'd be willing to relax the BAB requirement a bard with the dawnflower dervish and songhealer archetypes could be excellent both at healing and archery.
Dumping all your mental stats makes a character I wouldn't want to play, but that is the entire strength of the scarred witch doctor archetype. You can mitigate it slightly by playing a half orc instead, by RAW they should be able to take any orc-only options like archetypes.