Try this build. I've used it extensively for several months and I'm still very happy with it. But it does not fit your requirements because it does not include parry and BS/SD is so strong that I never had to care about attack chains. 
Hero Plan by Mids' Hero Designer 1,601
http://www.cohplanner.com/
Click this DataLink to open the build!
BS_SD_neu2: Level 50 Magic Scrapper
Primary Power Set: Broad Sword
Secondary Power Set: Shield Defense
Power Pool: Fitness
Power Pool: Leaping
Power Pool: Fighting
Power Pool: Speed
Ancillary Pool: Body Mastery
Hero Profile:
Level 1: Hack
- (A) Mako's Bite - Accuracy/Damage
- (17) Mako's Bite - Chance of Damage(Lethal)
- (23) Mako's Bite - Accuracy/Damage/Endurance/Recharge
- (46) Mako's Bite - Damage/Endurance
- (46) Mako's Bite - Damage/Recharge
- (46) Mako's Bite - Accuracy/Endurance/Recharge
- (A) Luck of the Gambler - Defense
- (40) Luck of the Gambler - Recharge Speed
- (43) Luck of the Gambler - Defense/Endurance
- (43) Resist Damage IO
- (43) Luck of the Gambler - Defense/Recharge
- (45) Resist Damage IO
- (A) Scirocco's Dervish - Accuracy/Damage
- (3) Scirocco's Dervish - Damage/Endurance
- (3) Scirocco's Dervish - Damage/Recharge
- (37) Scirocco's Dervish - Accuracy/Recharge
- (40) Scirocco's Dervish - Chance of Damage(Lethal)
- (40) Scirocco's Dervish - Accuracy/Damage/Endurance
- (A) Luck of the Gambler - Defense/Endurance
- (5) Luck of the Gambler - Defense
- (5) Luck of the Gambler - Recharge Speed
- (45) Luck of the Gambler - Defense/Endurance/Recharge
- (A) Numina's Convalescence - Heal/Recharge
- (7) Numina's Convalescence - Heal/Endurance
- (7) Numina's Convalescence - Heal
- (15) Resist Damage IO
- (15) Resist Damage IO
- (17) Steadfast Protection - Resistance/+Def 3%
- (A) Gaussian's Synchronized Fire-Control - To Hit Buff
- (9) Gaussian's Synchronized Fire-Control - To Hit Buff/Recharge
- (9) Gaussian's Synchronized Fire-Control - To Hit Buff/Recharge/Endurance
- (11) Gaussian's Synchronized Fire-Control - Recharge/Endurance
- (13) Gaussian's Synchronized Fire-Control - To Hit Buff/Endurance
- (13) Gaussian's Synchronized Fire-Control - Chance for Build Up
- (A) Recharge Reduction IO
- (11) Recharge Reduction IO
- (A) Run Speed IO
- (A) Defense Buff IO
- (A) Endurance Reduction IO
- (A) Numina's Convalescence - Heal
- (19) Numina's Convalescence - Heal/Endurance
- (19) Numina's Convalescence - +Regeneration/+Recovery
- (42) Healing IO
- (A) Performance Shifter - Chance for +End
- (21) Performance Shifter - EndMod
- (21) Performance Shifter - EndMod/Accuracy
- (23) Endurance Modification IO
- (A) Defense Buff IO
- (A) Obliteration - Damage
- (25) Obliteration - Accuracy/Recharge
- (25) Obliteration - Damage/Recharge
- (31) Obliteration - Accuracy/Damage/Recharge
- (31) Obliteration - Accuracy/Damage/Endurance/Recharge
- (34) Obliteration - Chance for Smashing Damage
- (A) Mako's Bite - Accuracy/Damage
- (27) Mako's Bite - Damage/Endurance
- (27) Mako's Bite - Damage/Recharge
- (29) Mako's Bite - Accuracy/Endurance/Recharge
- (29) Mako's Bite - Accuracy/Damage/Endurance/Recharge
- (31) Mako's Bite - Chance of Damage(Lethal)
- (A) Blessing of the Zephyr - Run Speed, Jump, Flight Speed, Range
- (48) Blessing of the Zephyr - Run Speed, Jump, Flight Speed, Range/Endurance
- (50) Blessing of the Zephyr - Knockback Reduction (4 points)
- (A) Empty
- (A) Obliteration - Damage
- (33) Obliteration - Accuracy/Recharge
- (33) Obliteration - Damage/Recharge
- (33) Obliteration - Accuracy/Damage/Recharge
- (34) Obliteration - Accuracy/Damage/Endurance/Recharge
- (34) Obliteration - Chance for Smashing Damage
- (A) Obliteration - Damage
- (36) Obliteration - Accuracy/Recharge
- (36) Obliteration - Damage/Recharge
- (36) Obliteration - Accuracy/Damage/Recharge
- (37) Obliteration - Accuracy/Damage/Endurance/Recharge
- (37) Obliteration - Chance for Smashing Damage
- (A) Aegis - Resistance/Endurance
- (39) Aegis - Resistance
- (39) Aegis - Resistance/Recharge
- (39) Aegis - Resistance/Endurance/Recharge
- (45) Aegis - Endurance/Recharge
- (A) Defense Buff IO
- (42) Defense Buff IO
- (42) Red Fortune - Defense/Endurance
- (A) Recharge Reduction IO
- (A) Performance Shifter - Chance for +End
- (48) Performance Shifter - EndMod
- (48) Performance Shifter - EndMod/Accuracy
- (A) Recharge Reduction IO
- (50) Recharge Reduction IO
- (50) Recharge Reduction IO
Level 1: Brawl
- (A) Empty
- (A) Empty
- (A) Empty
Code:
| Copy & Paste this data into Mids' Hero Designer to view the build | |-------------------------------------------------------------------| |MxDz;1404;688;1376;HEX;| |78DAA5934B6F125114C76778382D0C054A5B5AFA80B6D4BEA7A5BAF0B130A9D5A44| |949AAA35DA9640AB780122080B6D58D1FC0950B5DB9D3AA1FC1F84DD46FE203CF39| |FF0B49E3D209FC7F73CF3DE79EFFDCB9933FD9B10DE3E50DC31CBA59F3DAED825B6| |C79CDA66A05F35EB95A0C6DBB0577A750574FB72CC33052BDD9425ED59472B65B0D| |AF54708F1BAD52BA3FB5A38E54BDAD1CB75255B5526F18DFAD57544BD53B4EEFC6D| |E6F346ACEED6AA7AEDA6D0CF694D7ACD6CB113D53AE7468149291DB54AA14BFD5AC| |169DED46E9B490F7DA1DD53A1D2757CBF42FB03DB9BA41E3889033624F04638F05E| |B65A0025405A108C1D4552326871647052B31604DF256E2325AC3C8B374115599CF| |24E43B064E04D953C1E20BE0B9204CBDFCE8E5F763F5005A06D0722D21B0292FA83| |D055D095DB803DC170CC185462C49C169E3903C59DA93F5DEC733031F803341E8A3| |C0FE047C1644A8D7207A9983ABD81220488B85316384D7B191148AE85064061EA83| |E6A0E48283A2B218BB2E2FA31E3303C0CFBC30782E5ACE40D505E42E725DE8A9B91| |D7C01BC15846F2A2D46254771D455745A549FDACC99F923CFE0BF82D98F9037405B| |3869F71445513BA6A022724853391C29998C29998C27999C1E94952D524AA7C93DF| |64BD8DEF82DC0F8169F1F6C3DF74972EA34C91B46E9486BD0CEC65602F037BB3E7E| |CC5E939E774D51CAAE651358FAA795465519545959F7A2D6077020B9BB2BF172F03| |39E012CED6164E1AA52F21DDB784CD5CD60849824BABAEEAA759C5493823638EAE7| |1F0A236F0A236F0A2E668D14D9DB0899ADC394C05FADF26FD788BF6FE89EC07FADF| |94614A241DE87F9BFF757DB17BEB0CDE0D91DE63D927310FF8EE01CB431E3EE23B8| |FEF0E598A3CEC7EB57B4EA357D8D055966B2CD7595E7192152609B3D82C11962196| |284B8C25C132C6926279C7D2FD0B97660040| |-------------------------------------------------------------------|
Assuming an Achilles Heel proc in Hack, the best single-Parry chain is Parry > Hack > Headsplitter > Hack > Disembowel, which requires 219% recharge in Hack, 108% in Headsplitter, 38% in Disembowel, and 0% in Parry.
A single-parry chain with a slightly lower global recharge requirement would be Parry > Headsplitter > Hack > Disembowel, requiring 172% recharge in Headsplitter, 77% in Disembowel, 31% in Hack and 0% in Parry.
This is my current build for Sapphic Neko. Works very well, the only drawback is that it relies on parry for melee defense, but so far i've never had a problem with that. I have soloed ITF with this build, so i do feel like it's working 
Also, i despise having to take fighting pool, so this build works without it.
She is a hover-scrapper, so if you don't wanna hover, change those to something else.
Hero Plan by Mids' Hero Designer 1,621
http://www.cohplanner.com/
Click this DataLink to open the build!
Sapphic Neko: Level 50 Natural Scrapper
Primary Power Set: Broad Sword
Secondary Power Set: Shield Defense
Power Pool: Fitness
Power Pool: Flight
Power Pool: Speed
Ancillary Pool: Body Mastery
Hero Profile:
Level 1: Hack -- Mako-Acc/Dmg(A), Mako-Dmg/EndRdx(3), Mako-Dmg/Rchg(3), Mako-Acc/EndRdx/Rchg(5), Mako-Acc/Dmg/EndRdx/Rchg(5), Mako-Dam%(7)
Level 1: Deflection -- S'dpty-Def/EndRdx(A), S'dpty-Def(7), S'dpty-Def/EndRdx/Rchg(9), Aegis-ResDam/EndRdx(9), Aegis-ResDam(11), Aegis-ResDam/EndRdx/Rchg(11)
Level 2: Slice -- Sciroc-Acc/Dmg(A), Sciroc-Dmg/EndRdx(13), Sciroc-Dmg/Rchg(13), Sciroc-Acc/Rchg(15), Sciroc-Acc/Dmg/EndRdx(15), Achilles-ResDeb%(17)
Level 4: True Grit -- S'fstPrt-ResDam/Def+(A), Numna-Heal(43), Numna-Heal/EndRdx(43)
Level 6: Swift -- Flight-I(A)
Level 8: Parry -- Acc-I(A), Acc-I(17), LkGmblr-Def/EndRdx(19), LkGmblr-Def/Rchg(19), LkGmblr-Def(21)
Level 10: Active Defense -- RechRdx-I(A), RechRdx-I(23)
Level 12: Battle Agility -- RedFtn-Def/EndRdx(A), RedFtn-Def/Rchg(23), RedFtn-EndRdx/Rchg(25), RedFtn-Def/EndRdx/Rchg(25), RedFtn-Def(27), RedFtn-EndRdx(27)
Level 14: Health -- Numna-Regen/Rcvry+(A), Numna-Heal(29), Numna-Heal/EndRdx(29), RgnTis-Regen+(46)
Level 16: Build Up -- GSFC-ToHit/Rchg(A), GSFC-Rchg/EndRdx(21), RechRdx-I(31)
Level 18: Whirling Sword -- Sciroc-Acc/Dmg(A), Sciroc-Dmg/EndRdx(31), Sciroc-Dmg/Rchg(31), Sciroc-Acc/Rchg(33), Sciroc-Acc/Dmg/EndRdx(33)
Level 20: Stamina -- P'Shift-EndMod(A), P'Shift-EndMod/Rchg(34), P'Shift-EndMod/Acc(36), P'Shift-End%(36)
Level 22: Against All Odds -- EndRdx-I(A)
Level 24: Phalanx Fighting -- Ksmt-ToHit+(A)
Level 26: Disembowel -- Mako-Acc/Dmg(A), Mako-Dmg/EndRdx(37), Mako-Dmg/Rchg(37), Mako-Acc/EndRdx/Rchg(37), Mako-Acc/Dmg/EndRdx/Rchg(39), Mako-Dam%(39)
Level 28: Hover -- Zephyr-Travel(A), Zephyr-ResKB(36), Zephyr-Travel/EndRdx(39), Frbd-EndRdx(40), Frbd-Fly(50)
Level 30: Fly -- Zephyr-Travel(A), Zephyr-Travel/EndRdx(40), Zephyr-ResKB(42)
Level 32: Head Splitter -- Sciroc-Acc/Dmg(A), Sciroc-Acc/Rchg(33), Sciroc-Dmg/EndRdx(34), Sciroc-Acc/Dmg/EndRdx(34), Sciroc-Dmg/Rchg(42), LdyGrey-%Dam(42)
Level 35: Shield Charge -- Armgdn-Acc/Dmg/Rchg(A), Oblit-Acc/Dmg/Rchg(40), Armgdn-Dmg/Rchg(43), Sciroc-Acc/Rchg(45), Sciroc-Acc/Dmg/EndRdx(45)
Level 38: Grant Cover -- HO:Enzym(A)
Level 41: Hasten -- RechRdx-I(A), RechRdx-I(48)
Level 44: Focused Accuracy -- GSFC-ToHit(A), GSFC-ToHit/Rchg(45), GSFC-ToHit/Rchg/EndRdx(46), GSFC-Rchg/EndRdx(46), GSFC-ToHit/EndRdx(48), GSFC-Build%(50)
Level 47: Physical Perfection -- Efficacy-EndMod(A), Efficacy-EndMod/Rchg(48), Heal-I(50)
Level 49: One with the Shield -- Heal-I(A)
------------
Level 1: Brawl -- Empty(A)
Level 1: Sprint -- Empty(A)
Level 2: Rest -- Empty(A)
Level 1: Critical Hit
Level 0: Ninja Run
I'd like to get to the softcap using 1 parry... what would the optimal attack chain be and what sort of recharge requirements would I need? (If there's a "pretty good" chain out there for less recharge I'd love to know as well"
also, potential builds are welcome