This deck is neat. You have easy starters, lots of consistency, and an insane grind game, and you can run lots of hand traps. The hand trap thing is what I like about this deck - it reminds me a lot of Dogmatika, where you can run a billion hand traps to slow your opponent down to the grind game, where you have an advantage. It's a little more comboish than Dogmatika, but generally just puts up a couple interruptions on the board, relying more on the searchable Trap and hand traps that a giant board. It's weird in that your "high end" board is just Apollo, but you search the trap and maybe DD Crow, and that's all you need.
The line-up is really simple. We're running 3 Rescue Cat because it is the best starter in the deck, and very needed now that Tenki is at 1. We play 1 Tenki to search Fraktall. Then we're on full playsets of Tris. The reason for this is simple, Fraktall is a 1 card starter, Kitt and Keras is a 2 card starter combo, and the extra Tri name in Nervall helps cheat out those link monsters. If I were to cut down on any of them it would be Nervall, because the Kitt + Keras combo is really good and means more of your hands actually go places, but I like just maxxing out on all my Tri names. There simply aren't enough Tri-Brigade monsters to skip on any of them. I also think you have to run 3 Revolt. Yes, you can search this card, but I think you need 3 for your grind game, and also you actually do want to see this card in your opening hand. Lastly, I run 1 Foolish. Foolish Burial full combo. Okay, admittedly, it's the weakest of your starters, but you have few enough starts in the archetype that I think if you're running pure Tri you should run this card.
Half the deck is interruption. That's the real appeal of this deck to me, that you can afford to run so many hand traps. DD Crow makes the cut despite being a little weak because it is searchable in your combos. Ash, Imperm, Veiler, and Belle are very generic hand traps that do just enough in most matchups, and double up as being the most common hand traps to hit with Crossout. Gamma is good offensively and defensively in this deck, and the deck can easily cycle through cards putting these on the bottom if you don't use them. It's just a good high-impact going second card that also protects a lot of your combos going first. Crossout is Crossout, if you're already running a suite of the most common hand traps I think this is obligatory, though I do contend not every deck wants to run this. (Yet. Maxx "C" would change that, theoretically).
The extra deck is pretty simple. 2 Barren Blossom, this is a combo piece and a consistency card in the extra deck, and I think you need 2. 2 Bearbrumm, you really need to search out the trap - this does lock you into Tris for the rest of the turn, so keep that in mind, but just use this to make Apollo at the end of your combo, you'll be fine. 3 Shuraig - you'll make 2 of these before your second turn sometimes, and so a third comes in handy for follow-ups. 3 also improves your grind game in a lot of situations where you only make 1 turn 1. 1 Silver Sheller - this lets you fire off your Trap in response to Cosmic or Twin Twisters and still get the interruption out of Shuraig, and comes up in some of your combos, but you really don't need a second. Apollo is your main boss monster going first, and we've also got Unicorn - Accesscode for going second. 1 Omega and 1 Lambda. You barely make Lambda, but Omega comes in handy since we're using Gamma defensively. Lambda does come up so I think it is worth the slot. We've got 1 Double Dragon Lords, you cheat this out for basically free in a lot of your combos and it puts up an interruption. If you're confused, you summon this card using your Tri-Brigade effects, so its link requirements aren't relevant. 1 Almiraj comes up in some low-end combo plays, I think you need this just to be able to play sometimes.
For the side deck, I'm running an artifact package. Lancea seems good right now, and also it hurts our deck pretty badly, so being able to send it with Crossout also feels good. It feels good enough in meta matchups that running the 6 with Artifact Sanctum makes a lot of sense, especially since it doubles as a Scythe, meaning you can lock out multiple types of decks going first, pretty sweet. Cosmic and Red Reboot are here for Backrow, and DRNM and Droplets are here for going second against combo boards.