If you were going to do a 2 level dip I'd suggest alchemist and grab extra arm.
Eldritch Archer magus because spell combat to buff yourself is good. Repeating crossbows only have 5 bolts in the case so there's no need to hurry to +6/+1 BAB, especially if you get rapid shot.
No, though it'd be a very reasonable house rule to allow it to reduce the loading time for a case of repeating crossbow bolts from a full-round action to a standard action, as with two-handed firearms.
Choose a type of crossbow (hand, light, heavy) or a single type of one-handed or two-handed firearm ...
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the character will be using 2 repeating one handed crossbows,Repeating Hand Crossbow
This weapon functions identically to a repeating heavy crossbow, except its damage, critical, and range values are equivalent to those of a hand crossbow instead.Repeating Light Crossbow
This weapon functions identically to a repeating heavy crossbow, except that its damage, critical, and range values are equivalent to those of a light crossbow instead of a heavy crossbow. Its significantly lighter construction and pull make it both more portable and more useful to those who rely on stealth or speed.Repeating Heavy Crossbow
You can fire a repeating crossbow with one hand or fire a repeating crossbow in each hand in the same manner as you would a normal crossbow of the same size. However, you must fire the weapon with two hands in order to use the reloading lever, and you must use two hands to load a new case of bolts.
Note the 'two hands required to use the reloading level' restriction, which makes dual-wielding repeating crossbows basically pointless if you don't have an extra limb (or a very lenient GM). Since you already get rapid reload as a bonus feat, repeating crossbows of the non-heavy variety are actually slower than their non-repeating counterparts (I don't believe the feat covers loading a new case of bolts).
Bolt Ace 5, Sohei Monk 6+
Flurry of blows with a crossbow, with weapon training crossbow and dex to damage.
A first level eidolon at sixth level is very fragile. Also, it will be medium size at most.
I would take brawler. Nothing says you cant martial flexibility into ranged feats.
I currently have Bolt Ace with a couple of levels of Freebooter(Ranger variant from Pirates of the Inner Sea), picked up crossbow path (for Precise Shot at L2) and is a Freebooter because Favored Enemy swaps out for a +1 untyped bonus to all party members in 30' against a particular designated target (requires a move action to 'paint' the target).
Sticking with Bolt Ace until at least L6 before seeing what all else to do.
I always recommend Weapon Master Fighter, specially since the advanced weapong training options came in. This is even better when you get your hands in some Gloves of dueling.
Three levels of that and you have it, with extra feats to net you anything else you may want/need.
The fighter also opens the weapon mastery feats, and burrowing shot is amazing. With 4 levels you are fulfilling the requirements for weapon specialization which leads to Point-Blank master, allowing you to shot in melee at ease.
Past that, you could look into other options and dips. Grenadier alchemist can be a solid choice to futher improve your ranged prowress and get another quick buff.