The Speed Runner achievement requires you to finish The Oak Shield's Demand mission in under 90 seconds. The mission is found in the Dawnstone Meadow area. This guide is to help those that are looking for the Speed Runner achievement. I'm sure there are faster ways to do it, but this is how I got it done.

In general, you probably need to take down all 3 cysts in 2 turns and avoid spells and skills with animations. The 3 cysts have 1 armor and 6 hit points, so I used piercing weapons and skills to take them out.

This guide assumes Easy difficulty.

Here are the gear and skills used for the run.

Leonhard

• Weapon - The Leech w/ pierce gems (video shows gems in recover, but those aren't necessary)
  
• Armor - Barbed Chainshirt w/ armor gems (might be optional)
  
• Accessory - Boots of Speed w/ speed gems
  
• Skill - Charge
  
• Skill - Action Surge
  
• Skill - Mobility

Aava

• Weapon - LongBow w/ pierce gem
  
• Armor - Deer Armor
  
• Skill - Advance w/ move gem
  
• Skill - Dash
  
• Skill - Mobility

Oiko

• Skill - Forcebolt w/ pierce gems
  
• Skill - Teleport
  
• Skill - Mobility

Mochizuki

• Weapon - Sword w/ pierce gem

Here is the step by step, there is also a video below that shows it.

1. Oiko move as far as possible to water
   
2. Oiko cast Forcebolt on Cyst 1 (3 points of damage, 3 remaining)
   
3. Oiko Teleport Leonhard
   
4. Leonhard move 1 square into water
   
5. Leonhard Charge bug
   
6. Leonhard finish move to near crypt
   
7. Aava move as far as possible over water
   
8. Aava Advance near crypt and target Cyst 2 (2 points of damage, 4 remaining)
   
9. Aava attack Cyst 2 (2 points of damage, 2 remaining)
   
10. Mochizuki move toward Cyst 1

1. Aava attack Cyst 2 (2 points of damage, destroyed)
   
2. Aava move into crypt
   
3. Aava Dash onto button
   
4. Leonhard move into crypt
   
5. Leonhard Dash to Cyst 3
   
6. Leonhard attack Cyst 3 (3 points of damage, 3 remaining)
   
7. Leonhard uses Action Surge
   
8. Leonhard attack Cyst 3 (3 points of damage, destroyed)
   
9. Mochizuki move toward Cyst 1
   
10. Mochizuki attack Cyst 1 (3 points of damage, destroyed)

The video is likely quite a bit clearer.

https://youtu.be/LopYBfJ3lrY