As a farming unit, Tutankhamun is pretty simple—you stick him in your frontline alongside another DPS, you use his first skill on whatever turn your DPS needs an extra 20% charge, and you have Tutankhamun NP on that turn. Since you can’t use Tutankhamun’s third skill, you have 70% battery available in-kit: 20% from Mana Loading, 20% from skill 1, and 30% from skill 2. You can make up the remaining 30% with a CE (if, say, there’s an event CE with starting charge) or with a Castoria Charisma. Since Tutankhamun’s NP also deals damage, he can help kill an enemy on turn 1 or turn 2 as well, though his unbuffed damage isn’t particularly high, so he won’t add that much to your damage ceiling.
There are two main drawbacks to using Tutankhamun to help with farming. The first (and smaller) issue is that it slows you down, since you’re adding an extra NP animation, two more skill presses, and another Servant swap into your farming rotation. The larger issue is cost—Tutankhamun is an SSR Servant, and even at max level, you can’t run five SSR Servants and six SSR CEs. You’re not likely to need Tutankhamun’s help farming unless you’re trying to farm a 90++ node, and those almost always need a damage-boosting CE on your DPS, so you’re capped at four SSR event CEs at most. At that point, you’re usually better off 6-drop farming the 90+ node, which is not all that hard for a developed box at this stage in FGO’s life.
This is to say, Tutankhamun is theoretically unique and theoretically useful, but in practical terms he’ll only rarely be “necessary” and the trade-offs for bringing him are such that you might as well just farm an easier node. There’s also the fact that if what you need is an extra push of ST damage, Soujuurou is free and outdamages an NP1 Tutankhamun even against Sabers, while if what you need is extra battery and buffs, Summer Chloe is an SR and does that better, too. Tutankhamun is only better if you need both of those things simultaneously, which is almost never the case.
As a primary DPS, Tutankhamun functions more or less like any other ST Arts unit, with the caveat that you need an extra guts in order to keep him alive for a full buff cycle. You can cover this need with a CE, a Mystic Code, or a Servant with targeted or partywide Guts. Each of these has drawbacks: relying on a guts CE means you can’t run Black Grail, while a Mystic Code guts or a support Servant with guts takes away your ability to bring a better third support Servant. Tezcatlipoca and Santa Night are both solid options as plug guts supports, but neither is as good a third support as someone like Tamamo, Lady Avalon, or Oberon—and then there’s also the fact that Tutankhamun cannot survive to a second buff cycle if you fail to secure the three-turn kill.
In exchange for all this awkwardness, you get literally nothing over using another ST Arts unit. Tutankhamun does have a lot of batteries, but so do Archuria, Hephaestion, Berserker Castoria, and so on. Tutankhamun’s base damage is a little higher than most other Archers, but Archers have low damage in general, to the point that Tutankhamun loses out to some neutral Servants (like Berserker Musashi) even before factoring in the support or CE limitations resulting from needing to find an extra guts somewhere. As a conventional Arts looper, he’s just… really bad. You’d genuinely be much better off bringing someone like Euryale or Tell.
If you’re farming, you probably want to give Tutankhamun an event CE, if you have one. Otherwise, Black Grail is your best damage CE, though yet again this runs into potential issues—your second guts source must provide a guts with more than 500 HP or else Black Grail’s demerit will just kill Tutankhamun anyway. This does have the mildly interesting side effect of triggering Tutakhamun’s star burst twice in a turn (once when the guts triggers and once when Black Grail’s demerit kills) but I doubt there’s any case where that would be practically useful tech.
While Tutankhamun doesn’t make good use of his cards, he has decent crit access on later turns if he’s triggering his own gutses, and he has almost no in-kit crit buffs, so crit damage CCs are a natural pick. He also gets a bit more value out of curse than most Servants do, so curse damage CCs are an okay option, though for the reasons mentioned earlier in the review curse damage is unlikely to make much of a difference in most fights.