The historical ending comes from just playing through the story mode-no frills needed. There's nine stages in this route, plus a tenth optional stage early on you might unlock (it's not needed, though).
To unlock the hypothetical route, you'll need to accomplish four hypothetical situations in early battles:
Getaway from Hulao Gate: Rescue Hua Xiong, who's way up in the north corner near the enemy's main camp and escape point. It'll be suggested as you make your way up there that you should rendezvous with him, but by that point it'll probably be too late (the message telling me he died appeared immediately after the game told me I should run up to meet him the first time I did the battle). Instead, once you defeat Chen Gong and get out into the "main" area in the southeast, just rush up there to his location-you should get a quick conversation and a "Hua Xiong is rallying!" message. (I believe he needs to survive the battle as well, but I've never seen him have an issue once he's rallied.)
Uprising at Chang'an: There's two here:
1. Make sure Wang Yun is alright. This one's easy enough-once Dong Zhuo's been defeated and Jia Xu shows up, just go back around to the northern drawbridge where you left him. He'll mention that he's going to go off and hide and then disappear, which is what you need. If you take too long, he'll retreat on his own, failing the objective.
2. Defeat all three groups of tigers. The first you'll walk right into on the main route, and the map will highlight areas where other groups are-they're not precise,, so if you go to those rooms and there's nothing there, check adjacent ones. I don't think there's a time limit on this, but doing it before killing Dong Zhuo will result in fewer enemies on the map, so you might as well get it out of the way.
Battle of Changshan: This unlocks if you beat all three tigers in Chang'an. It's a pretty simple one-just defend Yuan Shao three times. He runs north early on, stumbling into an ambush pretty quick up the path...and then a fire attack in the center of the map...and another ambush in the northeast. Just save him from all three of them. This is a fairly easy battle, and if you're playing catchup once you've beaten the historical route, Lu Bu and Zhang Liao will be high enough level to roll right over everything anyway.
Battle of Dingtao: If you've done the other ones, then Hua Xiong should be in your camp. Talk to him to start the battle, and you'll play the hypothetical version of it (which goes significantly better for your side).
Once Dingtao's been won, things will continue for four more stages down the hypothetical route, leading to that ending.
While you're doing all this, you might also want to take care of the hypothetical objective in the Battle of Shouchun, on the historical route. It's not needed for the endings, but you will need it for the "Crossroads" achievement. During the battle, Zhang Fei (who should be guarding your main camp) will disappear, reappearing in one of the corners to wreck some property-just get to him before he's done doing that and Yuan Shu gets too riled up. You should get two or three warnings before he's done.