Emiya Assassin CE

As an arts servant who generates a lot of stars, Another Ending is probably the best for Emiya Assassin. One that increases his crit damage is also nice.

I would second Another Ending if you intend for him to be your team Damager, but if your main goal is for him to be focused on criticals I would definitely recommend Leisure Strolling. Reason being that his star absorption is pretty low, so anything to boost that up will help him immensely, and the arts up is definitely important for him as it boosts his NP Gain (Which he wants badly) and his NP Damage. He can already get a pretty high critical modifier with his 2nd skill, so focusing on sustained Arts and Star Absorption are your better options.

If you ever plan on focusing on him being a Star Gen/support, however, Fragments of 2030 is the best CE you can put on him. Guaranteeing that even passively he'll generate stars, and when he does get some Quick/Busters off he'll generate that much more each round for your main carry.

Yea, it'll depend on how you want to run him.

If he's your main dps, then Another Ending would be good. Only downside is that his star weight is low so partnering him up with someone like Mash can be a problem. It's kinda remedied if you get lucky with cards tho. His brave chain can generate enough stars that it *kinda* doesn't matter. I have an Emiya myself and one problem is that he'susual good supports are casters liek Hans or Tamamo. which sucks coz you usually want to run Emiya vs Riders. nwei, still think Another Ending would be a good CE if his the main dps.

If you're planning to go for the crit generator route, then it's 2030. Budget option if you played at Onigashima event would be the Three Great Heroes. it gives star gen+, np damage+ and starting NP which are all great for him

Faithful Companions or Faithful Companions MLB is good. It helps with Art effectiveness and NP gain. Regular is 8% Arts effectiveness and 15% NP gain. MLB is 10% Arts effectiveness and 20% NP gain. PS it was a Onigashima exclusive

Okay, so I realize that all your CE's pick-up are focusing on improving Kiritsugu's NP gain, or Art-up

In my opinion it is not recommended to have Kiritsugu as the major DPS in fight because (1) you may already has Shiki as art-oriented Assassin with decent NP damage and NP gain and (2) Assassin class are in mediocre star adsorption of ~100, and 0.9 damage basic. Therefore, I dont really recommend to bring any Critical-Up CE for him, like Another Ending
However his unique 3rd skill and NP has amazing tactical merits, make him excellent in tough quest. Meanwhile, good hit account, high star generation basic with A+ Presence Concealment make him decent as demi hitter/support mixed servants in team.

Normally a CE's purpose is either remedy one servants's weakness, or enhance one servant's advantages.

So here is my suggestion
(1) Using Kiritsugu as the major DPS to riders, if you dont have NP5 Shiki, or other SSR assassins. Then Leisure Stroll is amazing for Kiritsugu. This CE is better than other art-up CE because it "almost" guarantee Kiritsugu will have critical attack, and a Crtical NP gain is doubled, then it is possible for a better NP generation of him.

For instance of AQA or AQQ chain of Kiritsugu (just versus normal enemy as example, not versus rider with 110% NP gain):
Projection (MLB, 20 Art-up): 23.74 AQA and 21.71 AQQ
Leisure Stroll (not MLB, 10 Art-up): 22.91 AQA and 21.44 AQQ. Only a slight different.
But....38.46 critical AQA and 35.51 critical AQQ
Even though a NPAA Art chain with 1st skill activated 40% Art-up, 44.82 for Projection, 42.59 (non-critical) or 58.92 (AA critical) for Leisure Stroll.
So that is the difference. Although more Art-up further enhanced Kiritsugu's damage of NP and normal Art-card, critical of normal card is more beneficial for many considerations like more stars and NP gains. Eventually Kiritsugu's 2nd skill and Quick card could be also utilized. What you have to do is to guarante Kiritsugu has enough star to adsorb, like equip 2030 for the rest of 2 teammates.

When your Kiritsugu are in high level NP and you want to have Waver and Tamamo to support him to shoot an amazing NP damage then spam his NP before Caster support's defeated, Art-up CE with high amount Art-up and NP damage shown more merit than Leisure Stroll.

(2) NP gain up versus pure Art-up (not Leisure Stroll)
From my own experiences, if not considering the NP damaging, I dont really suggest Art-up CE is better than NP gain CE for Kiritsugu just because his normal Art card is Sooooo bad, not shown superior NP gain than his Quick card. And RNG make him 2 Art card has less error tolerance like not forming Art chain to obtain additional 20% NP. Meanwhile, too much focusing on his Art card may make his good of star generation become less advantageous.
For instance, other team memeber's Art card as initial position, Kiritsugu's Art card will receive 6.4 NP at the 3rd position, but Quick card for 5.52. However, his Quick card can generate amount of stars which is beneficial for the team and make this 0.88 less NP gain less noticeable.
Hence to further utilize his Quick card and Extra attack with decent hit account, NP gain CE is not bad option for Kiritsugu, such as SR CE The Faithful Dog Who Waits, Kitchen-Patissiere.

Also, this is more applicable for Kiritsugu as demi hitter/support mixed rather than major DPS in (1). It wont necessary to bring such additional damage for his normal Art-card if not critical.

(3) 2030, Fox's Night Dream, or Chocolatier (Future)
Even though Assassins are famous for star generation, it is better to have additional CE for an stable resource of star generation, because RNG issue make Assassin's star generation by their Quick card less reliable. Also, Assassin has very mediocre star adsorption rate, if not equipped with star adsorption CE, you may find ~20 stars per round is not enough. So any round-based star generator CEs are always welcome, like 2030 as SSSR. Its 8 star is only a slightly less than Quick chain, but a Quick chain is RNG and not quite compatible for Kiritsugu instead of Jack/Shishou with Quick NP and 3 Quick card. Normally AQQ for Assassins is a better way to obtain NP as well as star generation, with 2030 you may make AQQ more versatile and flexible.
Or maybe my waifu's Fox's Night Dream if you have. Like (2), 20% NP gain for Kiritsugu is decent.

(4) His Rightful Place, Halloween Petite Devil, Azure Magical Girl, future CE like Dive to Blue etc.

Unlike Kaleidoscope with pure effect of starting NP, these CE can also provide some permanent or temporary effect like Art-up or NP-gain. It is a combination with 1-3, but beneficial for shooting his NP faster.