Total War: THREE KINGDOMS

The 5 Tiger Generals are

• Guan Yu and Zhang Fei, starting in Liu Bei's army
• Ma Chao, starting in Ma Teng's army
• Huang Zhong, starting in Liu Biao's army
• Zhao Yun, starting in Gongsun Zan's army

In addition, Liu Bei has a story event where Zhao Yun joins his team. There's a surprising amount of contention over how to trigger that story event though. The only things for certain are that it's triggered by some battle (most stories tend toward any battle, some tend toward a specific battle across the yellow river), it has a random chance of triggering, and that it has to be triggered in between turns 8 and 28. So if you play as Liu Bei and go past turn 28 without recruting Zhao Yun, either restart or pivot to a vassal/annex strategy against Gongsun Zan to get him.

As you might have guessed, I'll be using Liu Bei for this guide, but most of the steps can be done with any faction. If you haven't, I do recommend you also turn on timeless characters so that you don't have to deal with a hard turn limit on getting characters (Huang Zhong in particular is quite old).

In turn 1, follow the story. Have your extra undeployed character use a scouting assignment on Chang'an, Dong Zhuo's capital. This should reveal Ma Teng in your diplomacy window starting next turn. Ma Chao, his son, is still a child at this point, but he should come of age at turn 12, so we'll come back to him later. You can check on him by going to the court menu, going to the family tree, and then selecting Ma Teng from the known factions list. Sign a trade agreement with Tao Qian for more income, then end your turn.

Characters should start wandering in your court in turn 2, so also check the candidate list from time to time for any female characters (also look for champions, as the primary early game income will be from peasantry). Save up at least 4000 to adopt the female character (you'll probably need more to finalize the marriage deal). From this point, I followed the story to get Tao Qian's lands and build my economy up. After Lanya, I went northwest to take Donglai, you can start back east to take on Cao Cao instead. Make sure you're in range of an enemy army or settlement starting turn 8, then farm as many battles as possible until you get Zhao Yun.

At turn 12, go to the diplomacy menu and negotiate receive marriage with Ma Teng between Ma Chao and your female character. If you don't have a female character at this point, you can seek a spouse with Liu Bei (it's cheaper with the faction leader than any other character), then divorce and adopt her. Ma Teng will not be initially willing, but he shouldn't be too unreasonable at this point. Do this relatively soon, or else Ma Teng will find somebody else to marry Ma Chao to. Only one to go.

Start moving east and discover Liu Biao (do whatever you want with Cao Cao). At some point during, Tao Qian will probably have turned his lands over to you, giving enough prestige to rank up. Make sure you spend some points on army slots, as Huang Zhong is probably deployed as a general and any armies gained from annexation that go past the limit are automatically disbanded and possibly lost. When you find Liu Biao, you have a couple of options. You probably won't be able to unify even if you make them a best friend, but you can issue an ultimatum with the unify order (located under the war options menu after any other demand is selected). I think you can affect the chances of success by either raising their opinion or increasing your military strength, but I am not sure as the game doesn't show you the odds. The other option is to beat them down to submission, then unify if you can, or vassalize/annex if you can't. This might be the easier option if they become marked as an enemy of the Han, which automatically reduces both their opinion towards everybody as well as everybody's opinion towards them. Or you can spend points on spies and try to turn Huang Zhong by decreasing his satisfaction (he seems to have naturally higher satisfaction with Liu Biao, so this may not work without multiple spies).

Once you have all 5 Tiger Generals recruited, the achievement should pop.