Pick up 8 Rare Mods: Seems difficult at first glance, because Rare mods … well, they’re rare. They don’t necessarily drop that often. While it’s quite possible that 8 will drop as you do other challenges, this pairs PERFECTLY with an Index challenge, as all Index mods are Rare, and they drop frequently. TL;DR: go to the Index, if you can.
Kill 500 Enemies: Super easy, because it can be done passively! Don’t focus on this at all – it should just happen. If not, choose a high-level Exterminate and you should knock this out quickly.
Complete 3 Spy Missions: Again, an easy one, and again, one that you might be able to double up on with Invasion missions (if you’re lucky). This will work for ANY Spy mission, so keep an eye on the Sortie as well, because that might tick off one of these if you also need to do a Sortie challenge.
Complete 3 Sabotage Missions: Another super duper easy one, and one that can be doubled up with Invasions or Relic runs if that is also on the cards for that week (provided, of course, that there are Sabotage missions available). Otherwise, smash out three low level ones and be done with this in 10 mins.
Complete 5 Scans for Cephalon Simaris: Keep in mind that you will need to have a target assigned by Cephalon Simaris, so go see him at any relay first. Hopefully he’ll give you a common target. You can quite easily combine this with most other mission types, depending on the target you have, so ensure you have your scanners equipped.
Complete a Defence Mission reaching at least Wave 20: Not too hard, you just have to last a long time. That many waves is going to be at least half an hour, so buckle in – and remember, all you need to do is survive, so you should be fine with a good group. You can smash out a bunch of other passive challenges as well, so make sure you bring the right weapons to get multiple jobs done (if they are on the menu for that day/week).
Complete a Survival Mission Reaching at Least 30 Minutes: With a good group, this is actually quite easy. I’d recommend doing this while cross-referencing other requirements for the week, as you may be able to knock off a few passive challenges as well. Not too straining, but tedious if you don’t enjoy long(ish)-term survival.