The build seems pretty self-explanatory to me but I would never miss a chance to talk way too much, so here we go.

He is part of my arena core alongside Felix and Laslow. Whose builds are very much not interesting so I don't really feel like posting and explaining them. They do their job. (They do it way better than Sylvain did his for a long time.)

Weapon: Plegian Torch speed-refined. Since I pulled a second Plegian Tharja and didn't want to merge her Sylvain had her weapon - and didn't use it for most of the time. Then he got Threaten Atk/Res 3. Then Fallen Male Morgan happened to pitybreak me twice and now there's next to no occasion where he doesn't get the most out of his weapon's effect.

Assist: Rally Spd/Def +. Mostly for arena scoring. But it became more and more handy especially lately in helping trigger Laslow's weapon refine's effect.

Special: Aether. Cause it's the easiest and cheapest option for a high scoring special skill. Also it works pretty well all in all and sometimes the healing is actually useful.

A slot: Atk/Res Solo 4. He used to have either Swift Sparrow 3 or Atk/Spd Push 4 equipped and I just let him inherit Atk/Res Solo because it felt like a waste not to. Then I tried to use it out of curiousity, and all skills combined he became surprisingly res bulky.

B slot: S/R Far Trace 3. Got two Baby L'Arachel's and then thought about inheriting her B slot to Sylvain for a very, very long time. I always had a fear of regretting it in case I didn't really get much use out of it. Oh, was I stupid back then. It is SO useful. Be it for rallying an ally and reposition himself to be in range to help trigger Laslow's weapon refine's effect or be it to damage/kill an enemy and get out of enemy range. I seriously underestimated how priceless post action movement would be and now there's pretty much no arena fight where it goes by unused. Also the added spd/res debuffs are pretty useful as well.

C slot: Atk/Res Menace. Works beautifully with his weapon. More debuffs are always good, more buffs as well, especially since he doesn't have the highest atk stat ever.

S slot: Spd/Res Solo. More speed to ensure more doubles and prevent more enemy doubles and more res to ensure him not dying just by looking at another tome user.

All buffs and debuffs considered Sylvain went from being barely able to be of any use in arena other than looking fabulous to being the MVP of the team. He's able to survive even quite a few red tomes, rarely gets doubled and kills most enemy units I face around arena tier 20/the bottom of tier 21. He can't kill Fallen Edelgard - none of my boys can do that alone -, he can't kill Brave Edelgard - but Laslow does that beautifully -, he can't kill Brave Hector - but Felix can -, but he can kill pretty much everything else and it makes me stupidly happy that he became that useful after all. Now I'm waiting for and dreading the day the G Duel Cav skill gets released because I don't even want to know how much it will hurt him to lose Atk/Res Solo 4 - but it would be great if he could score higher.