In truth, Saigo does a fair bit of the thinking for you.

Generally speaking, the trick is to delegate: focus on the big enemies, and let your weapons' massive hitboxes take care of the zako. While it'd be wrong to call them "noise" - they are just as lovingly designed as the heavies - they're distraction hazards first, collateral second, there to convey the awesome body-shredding power later seen in Metal Slug.
I'm barely conscious of those Wolves or Ninjas, in what is probably Saigo's deadliest stretch of ground. It's not that they aren't a threat, I've died to them many times before. I just know that my x3 POW Kusarigama is wreaking such ungodly havoc with every shot, they're well accounted-for.
So my brain is freed up to track the obstructing Monk, his rear-guarding pal, and the Ryuichi I've just spoofed via terrain launcher. I know that once these three mobilise, they'll crush me like the Red Sea. So my job is to get us outta there ASAP, with the Kusarigama snuffing incoming fire. The brave kamikaze wolf that crashes into a Shadow? The formation wasn't conscious on my part, only the attack. If it'd hit me instead, it'd have been
autoguarded.I remember Round 3-1's bullet-sliced grassland well.

Dat DEIMOS!

Kusarigama is ideal there. Standing strike will annihilate rifles and their shot, guaranteed. Busts straight through the bullet and kills the sender. Don't crouch! There's no need, and it'll also preclude a POW swing (there will always be a POW drop near the checkpoint). Those not only wipe out Rifles in front, but behind too, as well as any airborne Browns, in one wicked sweep. Bunnyhop it for massive forward momentum - you're advancing at full throttle, and they're dying in droves. As with 6-1's Ninja/Wolf air support, I'm not really conscious of individual zako while crossing the haunted waste - my main concern is not landing smack in Ghost range for balls-to-brain bisection.
3-2 is a step trickier, and where Saigo really stops playing around. Again though, the delegation principle holds. I prefer the Katana here - nowhere as powerful as the Kusarigama, but its nice "umbrella" hitbox fends off the raining Wolves and Browns,
and buffets away Monks and their staffs. Yet again, it's the latter I'm focused on - the zako don't require specific targeting or spoofing, just a resetting blast now and then.
It's here that I think Saigo would've worked just as well as a mecha sidescroller, an arcade-ferocious Valken or Ranza. I'm the pilot, the weapons are the gunners, my job is to ensure we don't get blown out of the water while they shred incoming bogies. Once you develop this kind of faith in your weapons, it's much easier to focus on the advance.
God I love this game.

Alone On The Hellish Battlefield - and yet not!
TOTSUGEKIIIRound 4-1 is a different animal compared to Rounds 3 & 6's open battlefields. With its zako compartmentalised away, and the terrain uniformly flat, it's The Purple & Ryuichi Show. You have to master the former's attack timing and range, or you'll be set up for Ryuichi all day. Note that ceiling Purples will completely ignore you, unless you get on their turf, and also that while Ryuichi can follow you up and down, he's completely open while doing so.
It's all very orderly, in spite of the randomness.

Don't think of Saigo's melees as roiling chaos, but random assemblages of set parts. Stuff will appear in different places, and at different times, but by iron law, it'll always respond the same way.
^^^
1] Ryuichi Hop - you can get incredibly close and still beat his draw, jump acceleration is king. Never feel compelled to retreat!
2] Purple windup - note their significant delay. Note also their monstrous reach!
3] Ryuichi is
useless while transitioning between ceiling/floor.
4] Ryuichi Drop - trigger his X-axis while falling and get pointblank, he'll miss you by a mile.
EDIT: Ba-zing-a-ling-ling, that was smooth. Bizarrely enough, got a very similar Boney fight to my Max run, just without the opening stationary diagonal attack. Went for two mid-high volleys, didn't quite finish him off but just about made another pants-shitting rightward escape. Hmm. Mid Rank Boney's HP is low enough that you can stomp him pretty aggressively, though those bolts are always scary.
Was watching TV while doing this and bungled my st5 safe route, was flying completely blind all the way to the Shield ledge. Not to be taken seriously.

Trivia: always noticed but only just now confirmed, there's a crazy amount of input lag on the HS entry screen, on PCB, MAME and ACA alike. It seems like five frames at least. In-game commands are tight as can be, judging by MAME frame advance. Weird, thank god it's just there! Reminds me of Sunset Riders' bizarro 5f-delayed crouch input, despite everything else being next-frame.