Total War: THREE KINGDOMS

TLDR: either wait until you become an emperor and form an empire or skip to the last paragraph.

The White Tiger Confederation resource is based on how many allies you have (vassals don't count, whether yours or your allies'). To get max White Tiger Confederation, you need 8 allies simultaneously.

Getting allies can be kind of annoying in this game. After the first one, you're not allowed to negotiate the inclusion of other allies, they're done entirely by majority vote. And while they are more likely to go along with a proposal if they like the proposer, they also become less likely to go along with the proposal the less they like the invitee, and there's nothing you can do to affect their opinion of the other person (only Cao Cao can do that, but we're not playing as him). There's other aspects that make them less and less willing to accept a new member the larger that aspect is, including distance from the members, new total size of the alliance, and how much of a strategic threat the new member is (the last two seem counter-intuitive, but whatever). That combined with the fact that the longer the game goes, the more likely factions are to band with each other or get wiped out altogether make allying with anybody kind of a chore, even more getting 8 factions altogether. It's especially rough for bandits, who don't share most of the Han mechanics and generally have a harder time buddying up with them (and guess who you're playing as. Also, I mean, they're bandits).

It should be noted that you can bypass most of these rules by creating an empire, the last kind of alliance. ESPECIALLY nice is not needing a vote for new members, as only the alliance leader needs to approve them, allowing them to negotiate with each new member individually. This does require you to be at emperor rank though, so you will not be able to use this strategy until the end game, and will also still more than likely need to make quite a few concessions to get some of the medium-to-larger sized factions in.

Instead of all that, I used a trick from Shi Xie's playstyle. If you grant independence to an administrator, they spawn as a new faction directly under you as a vassal. If you liberate them, they become eligible for alliance treaties. This tends to increase their diplomatic opinion of you as well, while simultaneously decreasing your strategic threat. Then sign as many treaties with them as possible to increase their opinion of you even further (definitely non-aggression and military access pacts, which automatically increase a faction's opinion of you regardless of how good the deal is. I believe trade agreements do this as well, but bandits tend to get less trade agreement slots). You should probably do this with all 8 future members immediately, to benefit from everybody's immediate opinion bonuses and limit the risk of any geopolitical changes screwing things up down the line. Make a save before you liberate them just in case. Don't panic if your former vassals aren't immediately agreeing to a coalition. All of your positive treaties will increase their opinions over time, so skip turns and keep checking back in. If you need to decrease your strategic threat more, disband your armies. On the off turns, your allies might propose inviting others of their own accord. Accept them if you want, but keep the points from the second paragraph in mind if you still need more members (don't accept the single largest faction on the map). Also note that if objecting members are overruled, they will have an opinion malus towards both the people who voted against them as well as any future decisions made by the alliance. The AI tends to be more amenable towards coalitions instead of military alliances, but check both just in case. The White Tiger Confederation counter won't update until the start of the next turn, so end the turn when you get your 8th member and the achievement should pop on the start of the next turn.

Most of these notes and tricks should also apply to No Small Deed Left Undone.



Edit: So I tried this again for Liu Bei and had significantly more trouble this time, so I'm going to list some other things I found doing it the second time. First off, do this strategy as early as possible. If other factions become able to vassalize, they might steal your former administrators before you can get them into your alliance. The other thing is your military strength acts as a positive modifier to them joining, so keep at least one standing army around when inviting other factions, and more if your strategic threat won't reduce your relationship status with them. It won't help change the other member's opinions, but it might at least make the invitee more willing to accept. The last thing I found is that some characters when liberated seem to automatically form opinions of other factions, including other characters you liberate. So if one of your new vassals seems to start immediately at odds with all of your other vassals, you may want to cut them off instead (you can see their opinion by selecting them in the diplomacy window without entering negotiations).