Diaochan

EX Weapon: Chain Whip
Weapon Name and Skills: Graceful Aster - Cyclone: 10, Jubilation: 9, Vigor: 9, Roar: 8, Aggression: 8
Stage: Uprising at Chang'an
Requirements: Defeat Zuo Ling, Zhu Jun, Song Guo, Niu Fu & Hu Feng withing 4 minutes of starting the battle.

Rather easy objective as you can get it during normal stage progression.

Lu Bu

EX Weapon: Halberd
Weapon Name and Skills: Explosive Halberd - Thunder: 10, Fury, Swiftness, Velocity: 8, Harmony: 8
Stage: Recapture of Chang'an
Requirements: Defeat Zhenji, Zhang He and Yuan Shao within 10 minutes of starting the battle.

The timing can be a bit strict if you kill everyone in your way up to Zhang He. You will not need to worry about Chen Gongs unit as he and the ram will stay out of the Ballistas range and will generally not be attacked as enemies will go after you primarily.

Dong Zhuo

EX Weapon: Bomb
Weapon Name and Skills: Unavoidable Bomb - Inferno: 10, Vigor: 9, Frenzy: 9, Swiftness, Morass: 8
Stage: Ultimate Warrior Competition
Requirements: Defeat Sun Jian & Huang Gai within 6 minutes of starting the battle.

Rather easy objective as you can get it during normal stage progression.

Yuan Shao

EX Weapon: Extension Blade
Weapon Name and Skills: Twisted Crystal Spiker - Frost: 10, Jubilation: 9, Velocity: 9, Survival: 8, Protection: 8
Stage: Nobility Face-off
Requirements: Get the Yuan family recognized as number one within 10 minutes of starting the battle.

If you don't defeat all officers before Cao Cao or Sun Jian start over, you will need to defeat the indicated officers leaving Diaochan for last if you can to be regarded as number one for who can finish fastest. You can take as long as you need with the supplies units as they are pretty resilient. Wait for all the dialogue to finish for the treasure message.

Zhang Jiao

EX Weapon: Shaman Rod
Weapon Name and Skills: Possessed Staff - Venom: 10, Roar: 9, Enlightenment: 9, Awareness, Aggression: 8
Stage: Runan Rescue Mission
Requirements: Defeat Li Dian within 10 minutes of starting the battle.

Rather easy objective as you can get it during normal stage progression.

Meng Huo

EX Weapon: Gloves
Weapon Name and Skills: Manic Thunder Gloves - Thunder: 10, Roar: 9, Resolve, Spurt: 8, Harmony: 8
Stage: Protect the Animals
Requirements: Defeat Yuan Shao, Xiaoqiao & Yueying within 6 minutes of starting the battle.

Rather easy objective as you can get it during normal stage progression.

Zhurong

EX Weapon: Boomerang
Weapon Name and Skills: Enchanted Lotus - Venom: 10, Agility, Thorns: 9, Desperation, Rigidity
Stage: Protect the Animals
Requirements: Defeat Yuan Shao & Xiaoqiao before they get near the animals.

If you see the message "Quickly defeat Yuan Shao/Xiaoqiao, who is approaching the animals!" start over. Yuan Shao starts far from a Tiger the animal he goes for and due to level structure has the take the long way around to reach it. Xiaoqiao starts quite close to the Panda and can immediately head to it from where she appears.

Zuo Ci

EX Weapon: Talisman Cards
Weapon Name and Skills: Reality Destroyers - Inferno: 10, Triumph: 9, Aggression: 9, Protection: 8, Uplift: 8
Stage: Runan Rescue Mission
Requirements: Defeat Zhang He within 8 minutes of starting the battle.

Rather easy objective as you can get it during normal stage progression.

Chen Gong

EX Weapon: Art of War Scroll
Weapon Name and Skills: Divine Oracle Scroll - Flash: 10, Awe: 9, Rigidity, Fear: 9, Protection: 8
Stage: Clash at Guandu
Requirements: Defeat Zhang He within 5 minutes of starting the battle without a single allied officer being defeated.

At the start of the battle immediately make your way to Zhang Hes position at Yanjin, defeat Chen Zhen to open it's gates.

Lu Lingqi

EX Weapon: Crossed Pike
Weapon Name and Skills: Soaring Wings - Frost: 10, Protection: 9, Chain: 9, Fury, Greed
Stage: Battle of Xiaopei
Requirements: Defeat Guan Yu & Zhang Fei within 8 minutes of starting the battle.

Simple objective that you can do naturally through level progression. You will want to ignore all troops and go straight for officers. Personally lure Wei to the ambush point as they will eat up a lot of time getting there by themselves.