Because I seem to answer this question constantly despite the sources on them, a quick guide to completing the kill based weeklies:

Defeat 200 Normal Humanoid Enemies#

"Normal humanoid enemies" is defined as "the normal humanoid SF t-dolls you fight. All the time." So really, finishing this can be summed up as "play the game." This is really here for completion's sake but I expect people should NOT need help with this. Playing the game at all will complete this in short order. If you need help with this... then, I really don't know how to help you.

Defeat 200 Normal Machines#

Normal Machines are any non-humanoid SF units that do not possess an armour rating. Scouts, Dinergates, etc. all qualify for this. Chapter 6-3 has a set of Dinergates next to the spawn, consisting of 20 units of 5 each, giving you credit for 20 machine kills.

Spawn in, kill them, drop a dummy, withdraw your kill echelon, and repeat. 10 Repeats finishes the mission.

As an alternative, 7-2E not only has a high 3* drop rate (read: cores), but also spawns 14 prowlers and 6 scouts which you will run into while clearing the mission. This takes two turns with two high-level echelons, but also rewards you with a few EXP and a lot of cores.

For later game players, you can also do 8-1 Midnight runs instead for Dinergates and Tarantulas with Zas M21, which will can also be used to level units and get fodder for equipment enhancement so you might as well.

Defeat 10 Bosses#

A boss is... a boss. People really should not need help with this, but 3-6, 3-4E, 4-6, 4-4E, 5-6 and 5-4E lets you reach and defeat their boss in 1 turn. Yes, I realise this is like half the game. From 4 and 5 Deploy from the upper helipad, drop a dummy in your command post, and just go straight for their command post. For 3, drop off on any side Helipad and charge in. I will presume you know how to do routing. If you want to be cheap, you can defeat lower stage bosses as well, but it takes longer and is more tedious. 1-6 and 1-4E does allow you to get some normal machine kills on the side, but it's tedious. 5-6 is recommended because its 2 fights.

If you aren't on the Global or Japanese servers, you can also beat up Judge in chapter 9, who is also conveniently 2 spaces away from your command post and actually more entertaining.

Defeat 200 Armored Humanoids & Defeat 200 Armored Machines#

These go together because they're easily farmed in the same place. 1-4 Midnight is the easiest place given it has basically nothing but these 2 enemy types, and it's actually quite easy to farm it. It also gives you fodder for equipment enhancement.