Heroics can temporarily grant fighter feats, and Greater manyshot may not be necessary.
Manyshot itself has some awesome synergy with the Factotum, allowing a single Inspiration point to add Int to Damage for all four(eight if split) arrows at once.
Anyways, here's a very rough build:
Human Factotum 11/Chameleon9
Ability scores(32 pointbuy)
Int > Dex > Str > Con > Wis > Cha
28 Str [14+6 enhancement+4 inherent+4 Chameleon(6pts)]
28 Dex [14+6 enhancement+4 Inherent+4 Chameleon(6pts)]
18 Con [12+6 enhancement (4pts)]
34 Int [18+6 enhancement+5 inherent+5 levels(16pts)]
14 Wis [8+6 enhancement(0pts)]
14 Cha [8+6 enhamcement(0pts)
Flaws: Vulnerable, Inattentive
1- Able Learner(Human), Font of Inspiration(1st), Point-Blank Shot(Flaw1), Rapid Shot(Flaw2)
3- Font of Inspiration(3rd)
6- Font of Inspiration(6th)
9- Font of Inspiration(9th)
12- Font of Inspiration (12th)
15- Font of Inspiration(15th)
18- Font of Inspiration(18th)
Extra: Floating Feat is usually Font of Inspiration.
The above build lacks manyshot(which must be acccessed via Heroics), and has a total of 6(Factotum 11)+36(8*FoI)=42 Inspiration points.
760 000 gp total
Belt of Magnificence +6 (200k)
Unslotted Belt of Battle (24k)
+2 Splitting Energy Bow
Tome of Clear Thought +5(137.5k)
Manual of Gainful Exercise +4(110k)
Manual of Quickness of Action +4(110k)
Strongarm Bracers (6k)
652.100 gp used.
107.900 gp left.
HP: 19d8+88(173.5 average)
Move Speed: 30ft
AC: 18(10 base, +9 Dex, -1 flaw)
Arrow Nova: See below
Damage per Arrow: Minimum 2d6+18(can be improved via powershot and inspiration points)
BaB: 14(18 with divine power)
Base Saves: Fort +6, Ref +10, Will +6
Initiative: +21(before magic items/spells to improve it!)
*Assume Martial Focus and something else
*Cast Heroics three times(Power Attack, Manyshot, Greater Manyshot) <-(Eternal wands perhaps???)
*Cast Divine Power(not really necessary, only adds +4 to hit)
*Cast Greater Magic Weapon at 20 CL on your Bow(ask your caster buddy, get oils, whatever)
1. Win Initiative
Standard action: Manyshot(8 arrows at +28(18 BaB, +9 Dex modifier, +2 from bow, +4 competence from Martial Focus, +3 from GMW, -8 from Manyshot)
Swift action: Gain Full-round action from Belt of Battle
Standard action: Manyshot(see above)
Since you have 42 Inspiration points, repeat Manyshot 14 times via Cunning Surge(For a total of 16*8=128 arrows).
Move action 1&2(normal turn/Belt of Battle): Dance your victory dance.
Estimated Damage, assuming all arrows hit, and no criticals: 3.456(Damage per arrow: 2d8+2(bow)+9(str)+4(martial focus)+3(GMW)=2d8+18, or 27 average)
Power shot can increase this damage further, and I'm *SURE* that there are other ways to optimize damage output.
A dragonfire inspiration bard ally, for example, could augment this damage like crazy.
You may opt to use cunning surge less often, this allows for Cunning Breach(Ignore DR for 1 round) and Cunning Insight(Boost 1 attack or damage roll by +12(applies to 8 arrows at once).
You furthermore may opt to use Power attack with your bow at a 1:1 ratio(as described in the Energy bow's description).
If one chooses to replace the Chameleon Levels with Fighter levels instead, the acquisition of feats is easier and allows for more Fonts of Inspiration(requires other casters to buff you, though).