Previous: Locate the ID Card
Gear: Make sure that you've got the FIM-43 before attempting this mission.
This enemy can be annoying because it very rarely stays still long enough to launch an accurate strike against a specific part with the LAW. This is why the FIM-43 can make life so much easier.
Also, it will periodically launch Kidnapper drones against you. Although they can be shaken off if they capture you, the best strategy it to avoid them by keeping moving constantly. Eventually they will be recalled.
Whittle down its life bars, but try to keep some ammo left for attacking the AI Pod once Chrysalis has landed.
If you're re-playing this mission after having played Peace Walker Battle 2 and have a Rank 3 LAW and FIM-43 (and accurate shooting) it's possible to win without resupplying. However it pays to take a Supply Marker just in case ...
Late on you will need to get Chrysalis' railgun in order to finish ZEKE. In order to get it you need to win the fight without damaging the railgun. A good way to do this is to equip a light machine gun (PKM or M60 for instance) and go all out on the left wing of Chrysalis (the wing opposite the railgun). This way you can be sure that the railgun won't be damaged by any splash damage one of your rockets might deal.
Next: Travel to the Mine Base