Dead by Daylight

Although it would be most efficient to get this achievement with: Yoichi's Boon: Dark Theory since anyone in range of the totem you put the perk on will get the speed boost. I tested some other perks and found that they give you progress as well.
*As harleyqnzel said in the comments, in order to get progress with Boon: Dark Theory, the player getting chased by the killer has to be in range of the totem in order to get progress.*

There are only 2 perks to my knowledge that gives your teammates a haste effect which is a movement speed boost. The first perk is Cheryl's perk: Blood Pact. Whenever either you or the obsession are hurt you can see their aura and if you heal them or let them heal you, you give them a haste effect.

The second perk is Guardian (universal perk). When you unhook a teammate it gives them a haste status effect.

With Stranger Things now back, this is pretty easy to get by equipping Steve Harrington’s perk: Babysitter and then unhook survivors. Rinse repeat until the achievement pops. As of 12/10/23, tracking this achievement works.


BABYSITTER
VERY RARE STEVE HARRINGTON PERK
While you have a reputation for being self-centered, you risk it all to help those in need.
When you unhook a Survivor, they won't leave scratch marks or pools of blood, and they gain a 7% Haste status effect for 8 seconds.
You see the Killer's aura for 8 seconds.