AHA Conquest for Newfags
This guide was for the event as it was running. It will remain up as a reference, but it is not accurate to the archived version of the event available in the story tab.
TL;DR of the Mechanics
You claim tiles on the maps by beating enemies, or by doing nothing if they have no enemies. Some of the enemies are on bases which you can "analyze" (sweep) for rewards.
The team you set to analyze the base doesn't need to beat the stage, they can be all level 1. They also don't restrict you from using those students to fight. The only thing you can't do is assign a student to two bases at once.
The actual guide part
Zone 1
Step 1 is to just follow step 1 of the oldfag guide.
Follow this route:
The breakpoints for the bonuses are at 2, 4, and 6 students, so you don't need to stick a fifth one in there if you don't have a sixth to go with it. This is true for both the damage and reward boosts.
Clear out all the nodes on the route, then go to the lower base and assign 6 Gehenna students to it. Sweep it 42 times, costing you 210 AP.
If you don't have 6 Gehenna students, assign whatever ones you have, and then do however many extra sweeps it takes to get 250 of the currencies.
Then, remove them from that base, and put them in the boss base and give that the same number of sweeps. You want 500 of the first currency and an equal amount of the other two.
Borrowing assistant students for analysis does not cost credits so you should do it whenever it will help you.
Go to the shop and buy the Unlock Code for zone 2.
Zone 2
Once again, use the other guy's route:
That bear marked with a 68? You're almost certainly gonna need to sweep it more than that. It needs Hyakkiyako students. You should have Pina and at least one of Tsubaki, Chise, and Shizuko. You're going for 2k total on the second currency. Remember to use assistants. Join any public club, nobody minds if you're new.
If you have 3 or 4, you'll need 84 sweeps, totaling 1008 AP.
If you have 1 or 2, you'll need 110 sweeps, costing you an enormous 1320 AP.
If you have none of them, you'll need a staggering 146 sweeps, adding up to 1752 AP. Just do a couple rolls on whoever makes your dick harder between Toki and Nagisa, Pina is only a 1* student so you'll get her quick.
You can't cope by sweeping the other bases either. The Tier 1 bases give the same rewards as they did in Zone 1, and the Tier 2 bases need Arius or Commies.
Once you're done getting raped by your AP generation, go to the shop and buy the Unlock Code for zone 3.
Zone 3
This zone has level 60 enemies. Level 50+ shouldn't have problems. Level 40-50 you should be fine if you replace your tank with an assistant, or get an assistant DPS and use two healers. Below level 40 pray you have some level 75+ borrows that can solo the stages.
Here's the route again:
Follow the green offshoot when you get to it; you need to clear out all of the Tier 1 fights to unlock the boss, because it's also Tier 1.
Remember to bring your Chise, or whatever other blues you may have, to deal with the blue fights along the way.
Tier 1 fights are level 25 normally and 32 on bases, gray armor, and have a Millenium boost. Just stick Yuuka and Momoi in your team with whoever else and run them over.
Tier 2 fights are level 52 normally and 60 on bases, blue armor, and have a Trinity boost. If you're able to even reach this stage you definitely have both Serina and Yoshimi, there's your free 50% boost, smack 'em. If you rerolled for Mika last month, even better, just slap your free Hasumi in the squad as well and watch everything melt because you've just given Mika the equivalent to a color-match damage boost.
Tier 3 fights are the same level as t2, gray armor, and have an Abydos and Valkyrie boost. You probably don't have any Valkyrie units so just throw your free Nonomi in there with Serika and hope you can build a good enough team around them. SHoshino isn't the best choice, since you probably don't have a T4 bag to keep her alive yet and there are no red enemies to get the efficiency boost against, but Cost Recovery and an attack buff is acceptable if you also have a fourth Abydos unit to slot.
Zone 4
Level 70
This zone will unlock for free after the event ends, letting you read the story then without paying 2000 currency.
If you want to read the story a bit earlier, follow this path through it and then pretend it doesn't exist.
In most cases, it's probably not worth trying to fill out this stage, since a newfag will actually have more use for the lower-tier gear and materials.
You can skip unlocking it if you don't care.
Allegedly, some strong DPS students can solo the harder battles in this zone. If your club has max-level Iori, nyMutsuki, or similar, you can try using them to capture a few tiles. If you're already going in for the story, it might be worth at least trying to clear out the Tier 3 battle on the middle left to unlock the left side, then you can claim all of the blank tiles to get the Pyro boxes.
Erosion
All it does is refresh the battle on three random bases each morning. You can use the team that was in it for analysis to do the fight for free, or you can spend AP on it to use any students. Clear it out every day, it gives you Pyroxene, equipment balls, and reports.
Most Erosion battles are level 50, but some of them are level 30, and some are level 80. There doesn't seem to be any pattern to which tiles get which difficulty. Just throw in a team that can handle a level 50 battle and hope for the best, and if it doesn't work, you know to throw an assistant in there for next time.
You can't start a battle if your only striker is an assistant. You should have found this out while doing raids anyway, but apparently it's not common knowledge.
After spending 4,000 AP and waiting two days, every base in Zone 2 will be eroded. This happens to Zone 3 at 7,000 AP, then to Zone 4 at 10,000 AP.
Farming
Go to Zone 3 again. Make your way to the Tier 2 and 3 bases.
Zone 3 Map
If you can't clear the top ones, don't worry about it. They drop mainly T3 currency which only has gun materials and Voynich.
The Tier 2 bases give the same total currency amount, but it's spread out more. They have Trinity as their bonus school which makes them strictly better for most newfags, since getting 4 or especially 6 Abydos members is a bit of a task.
Analyze these with your AP each day. GET THE BLU-RAYS. Then go for whichever currency gives you stuff you want more. You're bricked out of 100%ing the shop anyway. Also note that each base has a different OOPArt that it drops, the rates are pretty good if you need them.
Upgrading bases costs event currency, and gives you Eligma and completes missions that reward Pyroxene. It's up to you whether you want to max out bases and fill out the maps for Pyros or farm for items in the shop.
Remember to just fill in the analysis team with whatever you have, then take it out and move it to another base when you go to analyze that.
Help, I can't even clear Zone 3
Welcome to Advanced Brickage.
You can try to farm Zone 2. Base 3-A is probably your best bet, it drops the two useful currencies and Nebras.
Zone 2 Map
Analyzing Tier 2/3 bases in Zone 2 does technically have the same ratio of AP to currency as the later zones, but the gear and material tiers are lower, and you're forced to bring Arius/Redwinter or Hyakkiyako for the bonus which you have experienced the pain of firsthand.