Credit: I got a lot of helpful information from this thread:
https://www.reddit.com/r/dynastywarriors/comments/xaroin/war...Pre-note: Infinity Mode is unlocked after clearing Ch. 5 (the end of the base game). It is also a higher difficulty, with time-limited challenges and (once past the 12 Zodiac Towers) the Miasma mechanic that was introduced in Warriors Orochi 3 Ultimate's Gauntlet Mode. You want to have your best top-power characters at max-Promotion and a high-upgraded Tier 4 weapon.
Pre-note 2: When you start this mode, you are given a set of 5 characters, BUT you can swap them for any characters you have unlocked from Story Mode. So... DO NOT TAKE ANY OF THE STARTING FIVE. You will not miss out on them, they stay unlocked (because those 5 are story-relevant for the mode, so this gives you the chance to have up to 10 characters right off). So, instead, take the rarest/most-powerful characters you already have. (Ryu Hayabusa, Orochi/X, Gaia, and any other of the DLC-added characters, other than Joan of Arc as she is part of the starting 5, are good picks.) This could save you some frustration later on, as all Warriors Orochi-origin characters are a bit tougher to find
and any from the WO4 Ultimate DLC don't spawn until the upper 25 floors of Sky Father Tower.
Technically, this achievement is straight-forward: Beat an enemy Officer and there is a chance they will join you. Yay! Do this 177 times (minus the 5-10 characters you started out with) and you are done!
---NEW OFFICERS---
To tell if a stage has a new character, the Level Select has a second screen that will give an Officer a golden highlight if they are one you don't have. (Main Officers are just guaranteed to be on the stage, they are the ones that populate it from the start.
Additional Officers may also spawn from the start and more can spawn as any are defeated, up to three spawns for each starting Officer. Except on Annihilation stages, there are no extra spawns there because that would be terrible.)
Also, while in a stage any Officer that you don't have unlocked will have a circle mark in front of their name (but not in menus, so you have to encounter them to see it).
You can tell if they join because they will have a happy voiced line and the text pop-up for it will have their name in blue instead of red. You can also review in the pause menu under Log, as it will state when a character joins you after being defeated.
Some characters appear to be restricted from being Main Officers, so aren't so easy to seek out. These are only characters of the Warriors Orochi 1-4 Forces, and even then many seem able to be Main Officers (for example, I've seen Da Ji, Fu Xi, and Dodomeki as Main Officers, but never Orochi, Ryu Hayabusa, or Gaia). While some of the restricted ones can spawn at any level (such as Orochi), the ones added in the WO4 Ultimate DLC seem to be either ultra-rare or only spawn in the upper levels (I have seen Ryu Hayabusa as low as lv. 82, when I got him, so I suspect perhaps either 80+ or 75+). As such, if you ever see them you should prioritize unlocking them before any other Officers to possibly save you some time and frustration later.
Finding these non-Mains can be a hassle. It seems that although characters can spawn on any map, they might have a higher rate on maps that they are associated with (for example, the one with the Yggdrasil tree seems to be fairly reliable for Mystic/God spawns).
---JOIN RATES---
As far as Join-rates go, it seems to start about about 20-30% (my rough estimate) and the only way to increase it is to beat the 100th level of Sky Father Tower. Doing so will increase Join Rate by +20%, so don't go nuts trying to farm everyone beforehand. Let that bonus help you mop up the rest.
It sounds like terrible odds, but in actual play it's not
that bad considering how often you'll be facing most characters over and over. Unless you minimize battles and focus only on adjectives and moving on from each stage, by the time you clear the 12 Zodiac Towers and reach the second stage of the setting, Sky Father Tower, you could easily have over 100 of the 177 characters noted for the tower. Halfway done and not even started on the worse challenge!
Really, just aim to recruit at least one of any that can be of the Main Officers for a level and you are good to go. You'll go through 160 stages (or as few as about 80 if you are able to regularly skip an extra level by clearing a stage quickly), so that alone would get you pretty close to having the entire roster unlocked.
There is, however, a useful trick. Once you locate a stage where a character appears that you are missing, you can virtually guarantee getting them!
If you defeat an enemy and they don't join you, you can pause and select "Start Over" from the menu under Victory Conditions. This will instantly reset the current level to how it was when you loaded in, with enemies in the exact same spots they started at. So, just rush over, beat them up, and then either finish the level after getting them or rewind time and try again (and again, and again, until you succeed).
---ADVICE, I GUESS---
Note: You should always prioritize collecting NON-Main Officers! You can always redo a stage to get a Main Officer, they are guaranteed to appear in the first set of spawns. But the others are not, and some can be rare. So if you spot one of those characters, get them first. Then, if you fail to get any Main Officers just finish the stage and restart it to get the rest.
Also, remember that once you have cleared a stage, any replaying of the stage is far more lenient for the timer. As soon as the goal is accomplished the timer stops (though, for Purify stages if any become corrupted again then the timer does resume. So I'd just look for any characters on a different stage instead.)
And if you are just not finding a character, you can always try the "reconstruct a battle" option by spending 25000 gems. It will re-randomize every floor of Sky Father Tower to have a new challenge, map, and Main Officers. It does not reset any of your progress, so you aren't forced to replay any levels to proceed.