This is my tried-and-true competitive Melffy deck built from years of testing (and accessible reprints). The greatest strength of Melffies is...their friendship and ability to work together! Because that gives them access to more boss monsters than any other deck I've built! So let's get into it.
You've got the obvious 3-ofs, Puppy, Catty, Pinny, then 1 of the rest because they're all searchable and do things Melffies need. Wally's at 1 because you only need to trigger her once. Rabby, as cute as he is, is sadly unplayable. Fortunately, the devs kept him relevant by featuring his adorable face on Staring Contest, which is a good mulligan card and permanently nerfs the monsters your opponent currently controls. Kalantosa gets kinda bricky if you have too many, but he's not even soft once per turn, so 2 is perfect, especially if you open with one and that 1 Fenny in hand.
There's a small danger package for removal/free summons because Melffies struggle to do all that on your turn. White Steed helps you build Dragite, which tops off this deck's negation alongside Herald of Arc Light, Apollousa, Impermanence, and Melffy of the Forest. Kerass is a ss that helps you xyz or link. Nimble Beaver's your primary ns target. No Rescue Cat because that thing is so handtrap prone that it is dead weight, and unlike Beaver, leaves you with nothing on the board. You also can't xyz or synchro with it. Because Melffies don't deal big damage on their first turn, you're totally safe skipping your battle phase with Evenly Matched before you build a big invincible board to smash 8000-0 next turn. I've done it more than once.
I:P Masquerena is especially great for these little beasties because they summon on opponent's turn, so after you've gone through Kalantosa, link with her. Knightmare Unicorn's your option if you couldn't field anything else. If you get 4 monsters, you can go into Apollousa or Underworld Goddess (with Goddess' effect, they technically use the same amount). Summon whatever's best for what you're facing. Masquerena cannot summon Tri-Brigades, though. That will have to be on your turn, but Shuraig can banish on your opponent's turn when your Melffies summon.
You may have noticed a peculiar pick that isn't any kind of beast in this deck. This is my most recent inclusion. I added Icejade Ran Aegirine because this deck has searchable water monsters, and Ran is a free Gymir summon. Previously, I had to get one of the lvl 8 Dangers or Alpha and make it with Pinny, but now I can just discard Pinny instead. Having Gymir on the field pretty much guarantees my victory. Unless you DRNM her, there's virtually no way around because she can trigger on anything, and if you chain her, she removes that, too. And if your opponent likes to banish, she comes back. Swordsoul Chengying is just an additional target for the Ran playset. The only downside to running her is you have to hard draw her, but even if you open on all 3 copies, that's not a total brick because you can also discard a copy of her for her effect. 1 Gymir is WAY better than 1 anything else.