Halo 4

As an addition to the guide of Briana11 VR46

This one can only be done on the map shatter, as it's the only map of the crimson map pack to house a mantis. You don't need to destroy it just boarding it unlocks the achievement.

Edit:
Since Briana11 VR46 deleted his/her guide;
The easiest way to board an enemy mantis is to carry an plasma pistol. Fire an overcharge shot at the mantis, preventing it from killing. Now you can safely board the mantis from behind while holding the "X" button, or the action button if you have an alternative button layout

Edit2: (Some small changes, thanks to the comments for pointing this out)
Also be ready to sprint to the mantis as players have the habit of jumping out from the mantis preventing you from boarding it.

This one is very simple. All you need is a Plasma Pistol wait patiently and overcharge the Mantis. Here is a Video that shows on How I Got it.

Board the Mantis, either by using a plasma pistol, making a session and boarding it whilst your friends are piloting it.

Or! ride a ghost and board the mantis before it stops you!

This achievement is needed to be done on Shatter.

Mantis's are located below the overpass at each teams spawn.
Mantis's are large and cause a racket you can see one from miles away, just be sneaky and board it whilst the pilot is immobilisers or caught of guard. Then Eurika! you have the achievement but the good news does not stop their, you get a second achievement for destroying it!
Pump yer Brakes and David and Goliath. Two achievements for an easy task!

David and Goliath - 20G (Requires Crimson DLC)

Difficulty: 2/10

This Achievement can only be unlocked after you have bought and downloaded the Crimson DLC.

Once you have done so, load up War Games, and play Crimson DLC.

When a game starts you will want to search the map for an enemy Mantis (looks like a giant Transformer or robot for those that dont know what a Transformer is.

Now approaching a Mantis can be difficult seeing as the pilot will try to shoot you with a machine gun or rockets from a distance. Also if you approach from the front, they can stomp on you.

My strategy works every time I play. Simply change your Load out to have Active Camouflage and a Plasma Pistol. When you see the enemy Mantis on screen or on Motion Sensor, simply crouch with the B Button and activate your Camo with Left Bumper and wait for it to get near. Then switch to your Plasma Pistol and hold down Right Trigger to charge up the shot and fire it at the Mantis after maybe 2 seconds. The Plasma Pistol's charge shot can temporarily stun all vehicles, including the Mantis, and you can tell by a light appearing around the Mantis and it will stop moving.

This is your chance, rush in and get behind the Mantis, then hold the X Button and you will board it, unlocking your Achievement.