1 Meter: HP double > light Truth Seeker > HP double > Shadow Mercy's Demise > Prophet's Bane ender (46%)
2 Meter: HP double > Shadow Mercy's Demise > Shadow Mercy's Demise > Prophet's Bane ender (52%)
( Damage calculation notes)
Notes: Arbiter struggles to reach level 4 ender if he counter breaks without any white life already on his opponent. The no-meter combo is very specific; Arbiter doesn't have enough time to do three heavy auto-doubles, so the last one needs to be a medium or you will risk getting broken. The 1-meter combo only barely gets to level 4, which makes it his best combo by a wide margin over the next. Because Arbiter doesn't have a shadow damage ender, spending 2 meters requires 2 shadow linkers. After any of these combos, you can add on as many as three Type-51 Carbine shots for an additional 2% damage each, so these combos can be 6% higher if you're willing to spend the bullets.
The Carbine magazine is one of Arbiter's most precious resources. Once you spend all 18 rounds, you cannot fire the Carbine for the rest of the match, so you must spend your bullets wisely! The good news is that there is almost never a bad time to shoot the Carbine. You can whiff punish moves from full screen easily. You can jump over projectile attempts and fire the Carbine from the air for strong damage; even if you land on the projectile, the trade will always be in your favor. Simply firing one shot from your Carbine on your approach can make your opponent hesitant to move. If you have an excess of Carbine bullets, you can add unbreakable damage to any combo or throw by tacking on shots.
Once you spend all your bullets, your HK normals don't fire the gun but instead do the command normals tied to heavy kick, and one of your most threatening options will no longer be available. There is a delicate balancing act between spending your bullets and saving them for later. Try not to die with a half-full magazine, but also don't spend all 18 bullets in the first round!
The fact that the explosion hurts you as well as your opponent makes grenades tricky to use. One common use is as a sort of pseudo combo breaker. If your opponent begins a combo while they have a grenade attached to them, they will have to quickly turn themselves projectile invincible somehow, or else the grenade will explode, stagger both players, and then the match will return to neutral. If you are applying offense, you can try to be out of range of the explosion, typically by using long range attacks like standing MP or firing Carbine bullets.
But the most common way to avoid the blast is to activate the Energy Shield, which prevents Arbiter from being hit by projectiles! If you can sticky your opponent with a grenade and then spend some shadow meter to put up your shield, you can apply pressure without worry of being hit by the blast. If your timing is good, you can even create "checkmate" situations using the Prophet's Bane command grab where your opponent must jump to avoid the grab, but then get recaptured by the grenade blast, while you are covered by your energy shield. There is lots of room for creative experimentation here, and it's a whole lot of fun too.
As an extra note, if Arbiter holds down and presses three punches (it cannot be down-forward or down-back), he will throw a grenade in front of his face which immediately explodes. This self-detonating grenade is invincible on startup and can act as a reversal attack, but it will stagger any grounded opponent it hits, including himself. However, if Arbiter is wearing his energy shield, he can use this reversal without being stunned by the blast.
As explained in the Plasma Grenade section above, perhaps the main benefit of Energy Shield is that Arbiter is not phased by projectiles while wearing it. He will still take the damage from all projectiles that hit him, but he can walk or move through them without entering hit stun. Because 7% damage is not very much, you probably will only be able to take one or two projectiles before losing all your shield's extra health, but it is always useful for Arbiter to ignore his own grenade blasts to continue his offense, or to move through troublesome projectile attacks like Glacius's Hail or Kan-Ra's Spike.
When Arbiter is not trying to start offense with expensive Carbine shots or Plasma Grenades, he takes a more standard grounded approach using his two opener special moves. Mercy's Demise is a rush punch-esque move that is negative on block, but decently fast and useful as a cancel off Arbiter's best mid-range buttons, such as standing MP. Arbiter always ends up point blank when he uses this move, though, and the medium and heavy versions are -6 on block and can be punished by every character, so you're best to stick to the light version, which is negative but not punishable by all characters, and still has decent range. It's worth noting that you cannot manual after Mercy's Demise; there is not enough frame advantage when the opener version is used, so you must start your combo with either an auto-double or a linker.
Truth Seeker is a long-range overhead move that starts too slow to combo after light attacks, but is often a better choice than Mercy's Demise because Arbiter retains advantage after blocked Truth Seeker. The light version, which can combo after Arbiter's medium punch buttons, is a good combo starter and leaves him at even frames if blocked. If you want to approach from further away, you can use the heavy version of Truth Seeker, which comes out slower but leaves Arbiter at +3 advantage, useful for throw or pressure mixups. Shadow Truth Seeker is projectile invincible, as well. However, Arbiter does not have a strong low threat, so you should likely default to a high block against him, since Truth Seeker is a common approach tool.
Arbiter tends to play a game rooted fairly strongly in the traditional Killer Instinct combo system. The main times he will start a combo without an opener is when his opponent gets hit by Plasma Grenade, which will work if the opponent gets hit on the ground or in the air. If Arbiter is wearing his Energy Shield, he can use Self-Detonating Grenade to stagger his opponent without staggering himself, and continue the combo unharmed.
Arbiter's linkers are fairly standard. Both Mercy's Demise and Truth Seeker have similar cadence and do similar damage as linkers, so it is largely preference as to which you use. Because Arbiter has slow energy sword attacks mapped to HP, and many of his HK attacks fire the Carbine, if you want to do a heavy manual after a heavy linker, you should use the Particular Justice (+HK) command normal, which is his fastest heavy normal by far. If you want to perform medium manuals, you should default to standing MK for similar reasons. Shadow Mercy's Demise is the higher damaging shadow linker, but it takes longer to execute, so if you need to squeeze some damage out of a late lockout, you'll need to use shadow Truth Seeker instead.
With no battery ender and no wall splat ender, Arbiter relies on his combo trait to add Carbine shots or Plasma Grenades after any ender to continue his offense. This is particularly useful after the Truth Seeker ender, because you can perform a flipout with standing LK and force them to deal with immediate pressure, which is well timed so that if you throw, the grenade will recapture them as they are tossed away. Prophet's Bane is a particularly strong damage ender, which is important because Arbiter does not have a shadow damage ender; trying to use shadow Prophet's Bane as an ender will always drop the combo and create a reset opportunity. You can tack on a Plasma Grenade after the damage ender too, but you will not have time to use his flip out.
In instinct, Arbiter gets a regenerating energy shield, which begins to recharge three seconds after the last time he was hit. If used smartly, this should give Arbiter 20% or more extra health, while also making him immune to projectile hit stun for his own Plasma Grenade offense. Arbiter can also press HP+HK to parry incoming attacks, which allows for a ton of creative applications. This is a true parry which covers high and low attacks with one input; you recover fairly quickly and can punish with an attack of your choice, and it is active on the very first frame so it can be used to parry meaty attacks if you choose. In fact, guessing with parry in neutral to catch a long-range poke or forward-traveling special move is a pretty good idea, since Arbiter's fast recovery means punishing the parry will prove very difficult. However, the parry does not have too many active frames, so if your opponent does not hit you at precisely the correct time, you will be open to counter attack.
Arbiter does not have an uppercut special move, so he must use normals to anti-air, and players will tend to jump against Arbiter often due to how well he controls space. Crouching HP is a giant anti-air sword stab, but it is rather slow and does not cover space above Arbiter's head, so it requires strong reactions and spacing to anti-air with. A better choice for anti-air is Particular Justice (+HK), which is faster and much beefier around Arbiter's head. You need to leave crouching block to use this normal, though, and if you accidentally press +HK, you will fire a Carbine shot which will miss from close range. Alternatively, you can try to air-to-air with Arbiter's good jump normals, such as jumping LK or jumping MP, which controls tons of horizontal space in the air.
Arbiter does not have a credible low threat. Crouching MK is his only low attack, and it causes a knockdown. You can special cancel it into Mercy's Demise, which will launch them, but you will not recover in time to combo unless an attached Plasma Grenade explodes with perfect timing, or you instinct cancel. This means that Arbiter will be less about high-low mixups and more about throw mixups, and defaulting to high block (since Truth Seeker is an overhead) is the best play against Arbiter.
Shadow Prophet's Bane is an interesting move. It is not invincible on startup, but as soon as Arbiter turns invisible, he cannot be hit or thrown by any attack. As long as you hold the buttons down, he will remain invisible (or for a set time), and then once you release, he instantly appears directly in your opponent's face and grabs them if they are grounded. The move has full screen coverage and will track you even if you change sides with Arbiter. To avoid this move, simply hold up (and keep holding up) until he releases it, since you cannot be grabbed while jumping or in pre-jump frames. However, it's not quite so easy if you have a Plasma Grenade on you, ready to explode and recapture your jump!
With the basic gameplan in play, look to expand into tricky setups involving tacked-on Plasma Grenades, standing LK flipout, and Prophet's Bane command grabs. In instinct, learn to make reads or reactions to shadow moves and parry predictable approaches, then punish. When all these elements come together, Arbiter becomes an excellent choice for players of all types, whether you like solid fundamentals and powerful projectiles or tricky trap-based mixups.