The only thing my mid refess loses to are mirrors, diondora/mystere, belt kingdom, and monsters. So I assure you monsters are quite good against refess. If the level 2 survives, it usually kills something. If you hit both row 2 units, that's 2 level 4s down with one level 2 on your field. The yuni is just a bit extra just to cement the win. You'll have plenty of chances to use yuni's skill. The whole file is mostly made up of level 2s and 1s with 3 units level 3, so once you get everything out by turn 10 or something, you stop playing cards (besides breath of the undead for 1 sp fire arrow kill at low gowen levels) and have sp to spam her skill.
See, most of the things out there right now are things that I've been playing and started playing way before it became "meta." So I know how to counter it. One card like fairy blessing or general's orders or miracle fruit or tree of hate or shade can really turn the whole match around. If you time a shade to drain falkow's sp to stop a potential return 2 turns later and at the same time dodge a violet ss and delay your salamander next turn for the owl, well, then you're just that much closer to winning. Course, that isn't as obvious as something like making gaiessoul backfire.
And no, I don't share files publicly. I usually don't share files on the guild forums either unless I'm done playing with them for the meanwhile. I hate it when ppl know my ss and when I only have 2 copies of something and take advantage of it (even though I take advantage of their's). To be fair though there were 3 matches where I recalled one of my opponent's ss (pom, lucia, and rasam) and timed a dragon breath iczer or sala iczer or forest of hate right when I knew it was about to trigger.
Ryu is 3 copies and then the whole mage soldier file falls apart. If you can sin or remove him, it's gg. They need more main units not just support.
For MD Aug, just put out ex cak or broken virus (who is a lot better than both of them combined) and she is donzo.
For overdose... you just have to get around that. It's a good thing monsters can take A LOT of damage.
For verlaat, remove him or tank him and then kill him. He's one unit. The main problem facing verlaat is that you have to be careful with his engage vs a really good player who times it to avoid sins, fiertes, field wipe ss, disengage ss, which I haven't seen yet.
For filebuilding, besides thinking about counters, think about opens too. Like for example alraune dryad seems really good vs mid refess, but then you think of lawtia. Most of them pack ebeeru ss 1st, which hits through alraune's defense and drains you 1 sp. Not something you'd want to do. Nor have alraune in your file at all actually.
Finally, the best thing about monsters and this takes a lot of getting used (I make dumb mistakes all the time) to is unit placement. You usually want to place your dudes mid row so you can put dryads and whatnot in front, unless you want the salamander to go in the back for extra damage. But sometimes if you really need to build up field, then you want to place them in row 1 so you have the extra space. They are really slow so use that to your advantage... won't be acting anytime soon. The level 2 will destroy if opponent doesn't attack, so that's good for you to stall too. If you have a sac unit like primrose with more agi, you can always move it back and then attack.