Evolve

Setup a solo game.
Map & Mode: Hunt - Wraith Trap
Effects: second monster
Extras: Favor Monster - Strikes 0
Play as monster

Drop down in front of your starting point. There are 4 dead colonists just before you. Eat them to get more shields. Go back and wait until the hunters drop.
Now crush 'em with your monster buddy and the round ends within 2 minutes. It should be easy with Level 2 banshee mines in their drop zone or play Goliath and kill them quickly. Concentrate on Medic and Assault!
With this method you can can boost too:
"Invicible" (Win a match in under 2:05 minutes)
"Counterstrike" (Attack a Hunter within 15 seconds of them deploying in Hunt outside of the Tutorials)
Do it 25 times and the achievement is yours.

I tried my best to write in English

---German---

Starte ein Solo Spiel
Karte und Modus: Jagd - Geisterfalle
Effekt: Zweites Monster
Extras: Monster-Vorzug - Strikes 0
Spiele als Monster

Lasse dich am Startpunkt vorne fallen. Dort liegen 4 tote Kolonisten direkt vor dir. Friss sie, um mehr Schilde zu erhalten. Gehe nun zurück und warte bis die Jäger droppen.
Mache sie einfach zusammen mit deinem zweiten Monster schnell fertig und die Runde endet innerhalb von 2 Minuten. Es sollte mit Banshee Minen wirklich einfach sein, wenn du auch noch Level 2 Banshee Minen in ihrer Absprungzone legst oder töte sie schnell mit Goliath. Konzentriert euch auf den Medic und den Assault!
Mit dieser Methode kannst auch noch folgende Erfolge boosten:
"Invicible" (Win a match in under 2:05 minutes)
"Counterstrike" (Attack a Hunter within 15 seconds of them deploying in Hunt outside of the Tutorials)
Mache dieses 25 mal und der Erfolg ist dein. :)

Hunt is currently the only gametype you can quickmatch for besides evacuation, though I have seen other gametypes pop up during the quickmatch lobbies.

Hunt is the 'deathmatch' style 4 hunters vs 1 monster.
The monster can also win by reaching stage 3 and destroying the power relay.
It's up to you what you play as. Playing as Hunters would probably be better served on a team, Monster if you're going solo.

Since the achievement is just for winning 25 matches, you should be able to private match this, in which case you could play as the monster and skew all the match settings in your favor. Personally I got this in matchmaking, so I'll give some tips.

Hunters
Assault - Since the main purpose of the Assault is damage dealing, as long as you're fighting you should be good. Make sure you use mines as Markov.
Support - Personally, I really like Hank. His orbital bombardment is so fun. Ive never really played or seen Bucket so I can't speak for him. Cabot's dust tagging is really nice. It's essentially the hunter equivalent of the monster's smell.
Medic - All medics work fine for Hunt, though I prefer the first one for the tranqs, as they also track the monster.
Trapper - Maggie is definitely preferred for Daisy to find the monster. I'd recommend against using Abe.


Monster
Goliath - If you're good you can win at stage one, or at least cause them to fall back enough for you to rank up. As far as I've seen, Evolving brings you back to around half HP (if you're below it) which is more than enough to fight the hunters with if you have armor. Personally I've never lost as the Goliath if I've been at least Stage 2. I always make sure to start with Leap and Charge to have more mobility. Not a bit fan of Fire Breath. Rock Throw and Leap are your friends.

Kraken - Can't speak much for this class. Seems you need to make really good use of his abilities.
Seems better when whittling the hunters down (strikes-wise) then going in for a final assault when they're all weakened.

Wraith - Seems to have an easy time reaching Stage 3 in hunt since it's so mobile. I rarely see Stage 3 Wraiths lose. Very high burst damage. Good at misdirection.


So while your best bet would be custom matches (as the achievement seems to make no distinction), if you'd prefer to do multiplayer that's obviously an option. The Goliath is really easy to learn and does great as long as it isn't a completely tight-knit team. Should be golden as long as you reach Stage 2.

Play as monster

Map: Fusion Plant
Map Effect: Second Monster
Round length: 5 minutes
Reinforcements Time: 2 minutes
Strikes: 0

Healer: Lazarus (he is worst of the healers, but excels in reviving and since strikes set to 0 he can't revive)
Support: Kayla
Trapper: Jack
Assault: any not upgraded

When you load in you should see a metal structure near you. There are 4 human bodies in there you can eat for armor. Wait for hunters to spawn then kill medic first. Between you and second monster you should be able to finish under 2 minutes.