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lv 8 Half-elve Summoner's eidolon
the build needs to Haste spell first round...and a healer
Does an Eidolon using natural attacks get an extra attack from Haste?
I have two evidences to say the answer is "yes"
3r official rulebook Draconomicon page 66
Dragons love haste, and not just for the extra (often sixth!) attack it gives them when making a full attack. A +1 bonus on attack rolls is often just that much more cushion for using Power Attack, since dragons rarely have much difficulty hitting their foes. A +1 bonus to Armor Class is always welcome, and increasing a dragon’s speed by 30 feet makes it outpace every opponent that much more.
and the Pathfinder Creative Director said "yes"
build
Form: Quadruped
HP: 51 (6d10+18)
AC: 30 (+2 Dex +14 NA +4 armour +1deflection -1 size)
Initiative: +2
Speed: 40 ft
Ability Scores: Str 30 Dex 15 Con 17 Int 7 Wis 10 Cha 11
Saves: Fort +10 Ref +9 Will +4/+8
Feats: Power Attack (1st), Weapon Focus: Claw (3rd), Improved Natural Attack: Claw (5th)
Evolutions (base): Bite, Limbs (Legs), Limbs (Legs)
Evolutions (extra, 15-point pool,+2half-elf,+2Extra Evolution feat): Large (4), Pounce (1), Claws (Legs, 1), Improved Damage (Claws, 1), Rend (2), Gore(2), Energy Attacks (2), Improved Natural Armor (1), Improved Natural Armor (1)
Special Abilities: Darkvision, Link, Share Spells, Devotion
Haste Attack Routine: bite +15 (1d8+3d6+15) and 3 claws +16 (5d6+15) and Gore +15 (1d8+3d6+15) and rend 2d6+15 if two or more claws hit.
melee Attack Bonus
+15=+6bab+10str+1magic fang (greater)+1Haste-2Power Attack-1size
melee damage roll
+15+3D6=+10str+4Power Attack+1magic fang (greater)+2d6Vicious+1d6Energy Attacks
base damage roll
bite:1d6=>large=>1d8
Gore:1d6=>large=>1d8
Claws:1d4=>large,Improved Damage,mproved Natural Attack=>2d6
Equipment:
Belt of Giant Strength +4 16000
Cloak of Resistance +2 4000
Amulet of Mighty Fists(Vicious) 5000
Ring of Protection +1 2000
average danage:2d8+23d6+90=179.5
dpr(AC 21,not including CH)
(2d8+6d6+30)*0.75+(15d6+45)*0.8+(2d6+15)*0.896=45+78+19.712=142.712
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Vicious isn't so good with all of those attacks; I'd reduce by 3.5 per attack and choose "Lightning"; Eidilons are hard to heal. I also believe the power attack is "not worth" the -2 to hit vs most foes, If this is PFS improved natural attack is NOT a legal feat (no monster feats in PFS).
But as a DPR Olympian seems very solid; Eidilons always do :).