So this guide is going to assume that you have everything unlocked, all of the relics, lore, traps, and classes. This is also not going to be a step by step guide, but rather a framework of how to complete these challenges. You will still have to make good decisions during gameplay, sorry.

Alright, weirdest one first - Horoscopeophobia.
Kill King Gigald while only ever choosing the top option when offered a boneraise, relic, or spell. No re-rolls allowed!

Recommended class - Sinned Demonologist
General Idea - Pick the top option every time you get a chance. The top option will usually upgrade your minions, and eventually get you demons. Don't pick anything else ever. Don't reroll. I have no idea if strangers are part of the challenge, but I took the top option whenever possible just to be safe.
Useful Relics - You don't get to pick, so...
Useful Minions - Again, you don't get to pick.

The one that requires the most set up - Alzheimer Survivor
Kill King Gigald having first forgotten 6+ Boneraise Lore, 6+ Heroic Force, and 6+ current Class Heritage meta!

Recommended class - Boneworm Brainiac
General Idea - We want to use the inherent power of the brainiac to keep all of their minions perfectly positioned on them to make this challenge as easy as possible. Boss fights are still gonna be rough. Get an Enboned Heart to help with HP and try to pick up some extra boss damage along the way.
Recommended Lore - to forget that is.
For Heritage I chose to forget all the temporary boost ones to start (Raisen Hasteum, Speedrun, Rejuvinate,) then Freshen Magilous, Freshen Melilous, and sadly Bossworm Basher. Spell scrolls are nice, but unnecessary, I hoped to offset the lack of HP scaling with an Enboned Heart, and I thought I could spare boss damage.
Boss damage ended up being the hardest part of the run, so if I were to do it again, I might forget the deamonic one and just double down on finding an enboned heart.

For Boneraiser Lore, I chose Diablos Incantation, Banishment and Sealment sigils, The Necronomicon, Scholastic Researcher, and Meldus Rituals.
I feel like meldus are the weakest of the three upgrade paths, but that's just my preference, and I often prefer to keep my demons instead of fusing them. Also you keep all the research that has been done when you turn of the researcher talent, so you only loose one spell scroll.

For Heroic Force, I turned of the waves I personally did not like, and the waves that do not drop bones. An example of each, I disliked the Torched Lantern wave (thank goodness for the nerfs,) and the slime wave only drops gems. Gems are nice, but exp and more minions take priority.
You can also turn off Strangers if you need one more.

This is by far the trickiest achievement, so good luck

I love the part where they said it's MELDIN TIME and totally melded all over those kings
Kill King Gigald using a legion that includes 3+ Meldus Minions, but no deamons nor giants (except Giantan Melds). No Meldum Afflicted class allowed!

Recommended Class Liche Necromancer
General Idea Step one, make sure you always have one level 2 and one level 3 minion.
Step two, spam level one minions until you see a melded minion. Keep an eye out for a meldus flame relic. Don't make a demon, and don't make a giant. Not even a bro Giant.
Step three, repeat steps one and two until you have 3 melded minions.
Step four, continue spamming level one minions
Step five, I lied about the step by step guide earlier
Step six, kill the king, dance on his crown.

So, you want to boneraise a legion containing 1+ Giantous Deamonous, 1+ Mighty Meldus, and 1+ Big Bro minions, eh? I do need to remember to put in a bold Big Boner Band.

First, Please make sure you have all the relevant unlocks, you won't be able to make the minions without the knowledges. When in doubt, make sure they are all on.

Then, please observe the graphic below for what exactly this all means:

First off, the Big Bro minion (top right) requires two of the same Bros, and then you need to mash the two together to upgrade them. That's the easy one.

The Mighty Meldus (top left) is the weirdest, it requires a level 3 and a lower level minion to be mashed together to get a Meldus minion. Then you need to mash two Meldus minions together to get a big Meldus. Once you have one of these, Just slap a hero soul in and get yourself a big stompy punchy Mighty Meldus friend.

The Giantous Deamonous (top middle) requries you go get a giant, then turn it into a demon. Any two minions, smashed into a giant, plus a third to get an upgraded giant. Then hero soul it into a giant demon. If you see bones being thrown around, you did it!

Do all three steps in a single run, and wham bam achivement. The best advice I can give is don't pick up your hero souls until you are ready to use them for upgrades. It will require a total of 4 souls, and there is a limited number on each run, so don't use them to raise something that doesn't progress the achievement.

Relics that make Bros or Melds more common can help, and getting a Meldum Serum relic can really speed you along.

Other than that, don't die. At least until you get the achievement - you don't have to win for this one, after all.

I'll keep this quick.
There's a shop that sells cards in the Clashful Cards menu. Check your collection to see what you are missing, then check the shop. Other than that, keep playing, and make the units you want to find the card of (disclaimer: I don't know if this actually helps.)

I've enjoyed this game, and I hope you are enjoying it too.
Good luck.

Lemme know if there are other tricky achievements people want a slapdash guide for.