Hello,
 I have been a fan of the series since the initial launch of "Demon's Souls" for the PlayStation 3. With this new addition of the "Dark Souls: Remastered", I'd thought I'd try and finally beat the game -- considering it's been many years and I still have never successfully beaten this specific title ("Dark Souls") ... I don't know what progressively became of the series` -- as I thoroughly enjoy them; however, when DSIII debuted ... I had the Credits Rolling in Less Then 4 Hours ..... WooAaaah...   .... inLight of this, I've been trying at "Rushing" Dark Souls. 
This is my Strategy, thusly:
-
Dark Souls
Dark Knight Halberd Rush
+The Mask of the Father
-----------------------------------------------
("*" = Optional)
Northern Undead Asylum:
100+
200 * Enemy | 5x Hollow = ~100~
280 * Enemy | 1x Undead Soldier = ~80~
2,280 - Boss | Asylum Demon = 2,000
Firelink Shrine: (~03:30~)
2,580 * Enemy | 5x Hollow Warrior = ~300~
2,660 * Enemy | 1x Undead Soldier = ~80~
2,720 * Enemy | 1x R.O.U.S. = ~60~
*Pick-Ups*
* 6x "Soul of a Lost Undead" = 1,200
- 3x Humanity
* 1x Ring of Sacrifice
* 1x Talisman
* 1x Morning Star
* 4x Cracked Red Eye Orb
* 4x Lloyd's Talisman
* 6x Homeward Bone
Graveyard:
*Pick-Ups*
* 2x "Large Soul of a Lost Undead" = 800
* 1x Cauduceus Round Shield
* 1x Winged Spear
* 1x Zweihander
* 1x Binoculars
New Londo Ruins
*Pick-Ups*
- 1x "Soul of a Nameless Soldier" = 800
* 1x Estoc
* 2x Transient Curse
Valley of the Drakes
- 1x "Large Soul of a Nameless Soldier" = 1,000
- 1x "Soul of a Proud Knight = 2,000
* Humanity
* 1x Astora's Straight Sword
* 1x Dragon Crest Shield
* Red Tearstone Ring
* Brigand Armor Set + Spider Shield
Darkroot Basin
4,520 - Enemy | Dark Knight = 1,800 <----- Dark Knight Halberd (~05:30~)
*Pick-Ups*
- 1x Grass Crest Shield
- 1x "Large Soul of a Nameless Soldier" = 1,000
- 1x Crystal Lizard (2x Twinkling Titanite +* 2x Titanite Chunk)
* Hunter Armor Set + Longbow
* Knight Armor Set
Darkroot Garden
5,220 - Enemy | 7x Ent = ~700~
5,580 * Enemy | 2x Possessed Tree = ~360~
5,660 * Enemy | 1x Frog-Ray = ~80~
8,660 - Enemy | 5x Great Stone Knight = ~3,000~
9,060 - Enemy | 4x Ent = ~400~
9,180 * Enemy | 2x Tree Lizard = ~120~
9,280 * Enemy | 1x Ent = ~100~
19,280 - Boss | Moonlight Butterfly = 10,000 (~10:00~)
*Pick-Ups*
- 2x "Large Soul of a Nameless Soldier" = 2,000
- 1x "Soul of a Proud Knight" = 2,000
- Elite Knight Armor Set
* 1x Wolf Ring
* Partizan
- Souls -
  6x Soul of a Lost Unead = 1,200
  2x Large Soul of a Lost Undead = 800
  1x Soul of a Nameless Soldier = 800
  4x Large Soul of a Nameless Soldier = 4,000
  2x Soul of a Proud Knight = 4,000
=============================================
= 30,080 - 26,590 (Level: 4 -> 21) [9+Dex, 8+Str] {*Rush=26,800*} [210]*
Equip(*) "Dark Knight Halberd" {Two-Handed}
- Fetch "The Mask of the Father" (+ Stone Set, Havel's Ring, & Ring of Favor and Protection) w/ "Grass Crest Shield"
_
I've calculated the Time Factor's (Roughly) ...
*With a "New Game", Rushing to the "Divine Ember" yields a prosperous 15,000 Souls. Killing things along the way and "Popping" Souls will satisfy the difference to equip the Black Knight Halberd right at the beginning of your game in only roughly ~10~ minutes of gameplay. At this point, things get finnicky.
Lately, I've been Reversing Hollow at the Firelink Shrine, rushing the Halberd -- if I don't get, re-do -- then hitting the Butterfly and Homeward Bone'ing back to the Firelink to immediately rush (Paladin Leeroy Drop) to Pinwheel at the effort of acquiring his mask. All-in-All, the whole effort takes a little less than ~15~minutes to Do--provided you get the Halberd.
 ***At both junctions though, I give up*** Should I risk the souls and rest at the following bon-fire in the Tomb of the Giants and get the Covetous Silver Serpent Ring?
Considering, there are only two ring-slots in the game available and I primarily intend to make use of (for the first playthrough) the "Ring of Favor an..." + "Havel's Ring" I think the other strategy may prove superior. Which is,
 *Spawn* 1. Rush Halberd | 2. Un-Hollow (Darkroot Basin Bon-Fire) | 3. DivineEmber+HomewardBone (Witch Beatrice) | 4. Havel's Ring | 5. (2nd Crystal Lizard) Taurus Demon -> Gargoyle's (Don't Ring Bell) | 6. "Ring of Favor and Protection" (After Acquiring Sunlight Medal Reward*) | 7. Reah/Patches (Pinwheel) ++Acquire "Mask of the Father" (Or Else, Re-Do) ~35:00~
...
...
The Problem Is, with Both Rushes -- I end up at the Covetous Silver Serpent Ring w/ 'x' Amount of Souls which I don't know how/what to do with ...
Other then Killing the Four Kings (In the Abyss) ... what all else is there I should do (Before Sen's Fortress)?
**Thanks**
 
 -EDIT-
With the exception of detouring for Snuggly's sake, going at a leisurely rate, and wasting a Homeward Bone from the Bone(*)Smith after upgrading the DarkKnightHalberd to Level+5 to be able to activate Paladin Leeroy, the process takes about 45 minutes to do (Including the Sif). At the moment though, the Rush just Leaves me with the First Bell waiting to be Rung and ALL Undead[Burg/Parish] Completed (Dragon/DarkKnights/Hog/etc.). Going further into the Tomb of the Giants seems to be a waste of time, as the door is "Locked by the Lords Power" (or something to that affect) -- So I always end up doubling back into New Londo Ruins, to kill an NPC holding a Key to Remove the Water and Access the Abyss ... This is about as far as I get, since from here I typically make effort to "Ring the Second Bell", and up lost in a Great Tree...
 
'gitGud