First of all, you might want to know what are the "cars" options.

Shokkjump Dragsta


Rukkatrukk Squigbuggy


Kustom Boosta Blasta


Boomdakka Snazzwagon


Looted Wagon


Grot Mega Tank


Deffkilla Wartrike

Roamin'
Travel 1km.


Kult of Speed
Travel 100km with any vehicle.


Roamin' Far!
Travel 1000km.


Roamin' Ded Far!
Travel 10,000km.


Proppa Wazza (Shokkjump Dragsta)
Travel over 150 meters in a single jump with the Shokkjump Dragsta.
(Find a ramp or hill, then combine warp movement plus acceleration)

Ramming Speed
Reach a speed of 200kph with any vehicle.
(Did mine with Boomdakka Snazzwagon, it has double acceleration: SHIFT plus F ability)

Ere We Go!
Reach a capture point first in Deff Rally mode.


Every now and then your team and rivals will race to a new checkpoint.
Be there first for the achievement!


Speedboss
Place 1st in the end of match race.
After the final checkpoint arena, everyone will whoosh to the finish line. Reach it first!

You can even drive straight to the exit gates some time shortly after the 4th checkpoint and score a slapping 100 points for your team!

Brutal Krumpa
Score 100 krumps.
(kill 100 players)

Kunnin' Krumpa
Score 1,000 krumps.
(kill 1,000 players)

Da Best Krumpa
Score 10,000 krumps.
(kill 10,000 players)

Fortress on Wheels
Get hit by 1,000 bullets with any vehicles.


BOOM!
Deliver the bomb.
(in the Konvoy mode)


Dakka Dakka Dakka!
Fire 100,000 bullets or other projectiles.


More Dakka!
Fire 500,000 bullets or other projectiles.


Endless Dakka!
Fire 1,000,000 bullets or other projectiles.



Surprize! (Looted Wagon)
Hit an enemy greater than 150 meters away with a Kannon shot 100 times.


Straight Shoota (Looted Wagon)
Hit 5 Kannon shots in a row 30 times.


Brutal Grot (Looted Wagon)
Direct hit and kill an airborne opponent with the Grot Bomm.


*Two tips how to get this one*
1) Semi-random method: in the Deff Rally, stay out of a checkpoint and fly the Grot nearby until some enemies are bounced/kicked up. A lot of players are being shovelled in the air, plenty of opportunities. That's where I got mine!


2) Semi-camping method: in the Konvoy, stay close to your Stompa, wait until it activates levitating laser - an enemy is lifted up - this is your chance.


Might Is Right (Kustom Boosta Blasta)
Score 10 kills or assists without dying with the Kustom Boosta Blasta.


Mork's Boom! (Kustom Boosta Blasta)
Hit an enemy greater than 50 meters away with a thrown Stikkbomb 30 times.


Flyboy (Kustom Boosta Blasta)
Score 15 kills while you are in the air with the Kustom Boosta Blasta.



Burn 'Em All! (Boomdakka Snazzwagon)
Ignite 2 or more enemies with a single Burna Bottle 200 times.


Might Is Right (Boomdakka Snazzwagon)
Score 10 kills or assists without dying with the Boomdakka Snazzwagon.



Might Is Right (Deffkilla Wartrike)
Score 10 kills or assists without dying with the Deffkilla Wartrike.


Get Stuck In (Deffkilla Wartrike)
Hit 2 or more enemies with a single Klaw swing 100 times.


Ded Sneaky (Deffkilla Wartrike)
Kill 75 enemies who have dealt no damage to you with the Deffkilla Wartrike.



Oi! Not Da Snacksquigs! (Grot Mega Tank)
Score a kill or assist on an enemy who has damaged a friendly Squigbuggy in the last 10 seconds 75 times with the Grot Mega Tank.

Too 'Ard To Die (Grot Mega Tank)
Take 1,000 damage without dying with the Grot Mega Tank.


Wrecka (Grot Mega Tank)
Damage 2 or more enemies with a single Plow hit 25 times.


Not an easy challenge and luck based.
Best advice I can give is to drive in with plow ready and hope for a hit, like in this video:

Orks Is Never Beaten (Shokkjump Dragsta)
Hit an enemy greater than 100 meters away with the Shokk Rifle 250 times.


Might Is Right (Shokkjump Dragsta)
Score 10 kills or assists without dying with the Shokkjump Dragsta.



Mob On Me, You Gits! (Rukkatrukk Squigbuggy)
Repair 10,000 damage on teammates driving heavy vehicles with the Rukkatrukk Squigbuggy.

Painboy (Rukkatrukk Squigbuggy)
Repair 15,000 damage on teammates with less than 50% health with the Rukkatrukk Squigbuggy.

Nitro Squigs (Rukkatrukk Squigbuggy)
Score a healing or damage assist on 15 enemies without dying with the Rukkatrukk Squigbuggy.

There are 8 "cars" at the moment, but you need to complete challenges "only" for 7.
In the top menu, click on Challenges, then on a vehicle, and you'll get a list of objectives:


Speed Freek (Rukkatrukk Squigbuggy)
Complete all Rukkatrukk Squigbuggy challenges.


Speed Freek (Boomdakka Snazzwagon)
Complete all Boomdakka Snazzwagon challenges.


Speed Freek (Grot Mega Tank)
Complete all Grot Mega Tank challenges.


Speed Freek (Deffkilla Wartrike)
Complete all Deffkilla Wartrike challenges.


Speed Freek (Shokkjump Dragsta)
Complete all Shokkjump Dragsta challenges.


Speed Freek (Looted Wagon)
Complete all Looted Wagon challenges.


Speed Freek (Kustom Boosta Blasta)
Complete all Kustom Boost Blasta challenges.

Mob Up!
Play a game with a party.
(Form a party and play!)

Orky Initiation
Use the "WAAAGH!" quick chat.
(In-game press 1, 2 or 3 to bring up quick chat. Pick "WAAAGH!")



Smoky Gubbinz (Boomdakka Snazzwagon)
Activate Billowing Smoke with less than half health 35 times.
(Drive near enemies, receive damage, whoosh away in a smoke, repeat 34 more times)