Requirements:
99 (or close to 99) Range, Defense and Magic
96 Summoning
75 (Rigour) or 92 Prayer (Soulsplit)
Overloads
Strongly Recommended:
Elite Enhanced Excalibur
Stopwatch - This is used as both a 15 second timer and 5 minute timer.
Royal dwarven gravestone (15 minute grave) and 99 summoning - In case of death you can bank and get your killcount within 12-13 minutes with a Steel titan.
Setup:
I won't include Pernix and Divine here ($$$), other than mentioning that they're far superior to Armadyl and Spectral.
What to consider when choosing armor is your range attack bonus and the magic defense bonus. Range defense is not needed, and the melee minion doesn't hit that often to justify a melee helm. What you decide depends on how much and what you want to risk. Based solely on stats and not considering risk, here's a hierarchy of items for each slot.
Weapon: Chaotic Crossbow > Rune Crossbow
Helm/Body/Legs: Armadyl > Karils
Shield: Spectral SS > Dragonfire > Blessed SS
Cape: Ava's Alerter > Ava's Accumulator
Necklace: Fury > Amulet of Ranging > Glory
Boots: Ranger's > Snakeskin
Gloves: Barrows > Black d'hide
Ring: Archer's (i) > Archer's
Ammo: Diamond (e) (Possibly Ruby (e) for start of kill, not sure if its ideal though)
This is what I use. Items kept on death are the Armadyl top and bottom, fury and Spectral SS. Risk is ~5M with protect item.
Inventory 1: Yak --> Unicorn
Method 1: Rigour
This is what I've been using, and its what I think works best. Quick-prays should be set to protect item, protect range and rigour. Before entering Overload, start the stopwatch, EEE Spec, brew to full HP and sip a restore. I wait the ~5 extra seconds until the overload repots to max before entering. Now simply kill Kree as you normally would.
Method 2: Leeches and Soulsplit
This should give longer trips, but slower kills. Haven't tried it myself though. Use the tactics to kill as above, only quickpray Protect item, Leech Defense, Leech Range and Leech Magic (unsure about magic), then when killing the minions Soulsplit flash to heal.
Tips and Tricks:
Earlier I mentioned a stopwatch, and starting it immediately after you overload. To maximize killing speed you want to know when your overload will "re-pot" you (every 15 seconds), and try to never sip a sara brew unless you're within 5 seconds of that time. If you need more healing than one sip try and start healing at 12-10 seconds before the re-pot. When doing this I brew 2-3 times and then super restore back to 99's and usually the overload re-pots within the next couple seconds. Also time brews so you can attack between sips, panic brewing is strongly frowned upon. Therefore if you start the stopwatch after you overload, every 15 seconds the stopwatch hits will be a re-pot time.
This is also used as a 5 minute timer for when the overload will run out. When the stopwatch is nearing 5 minutes you want your hitpoints to be below 590 (I try and stay between 500 and 650 at this time) so you can make the most of the overload running out. If you do it properly, and average using 10 sips of overload per trip (about what I'm getting), then you save 5,000 hitpoints of healing.
If you're struggling to kill the minions before Kree respawns to use the altar to restore prayer, the kill before you can use the altar only 3/4 kill the minions so you have plenty of time to kill them and restore prayer next kill.