Weapon plans are only obtained through Crates. You can only get these through daily challenges or by grabbing the supply drop and towards the end of each match and escaping. Each rarity of crate has a list of loot which must all be obtained before a new list appears. For example the white crate has 15 items meaning 5 crates must be earned before a new list will appear. The weapon plan icon has a large white square above the specific weapon. Not every new list will have a weapon plan in it, but there is a high chance for one especially in the first few lists.
EDIT: You can now get crates through the season pass by playing regularly and by donating food at the shelter.
You start out with 4 weapon plans (PM, Puukko, Silver Pigeon and the Thompson) meaning you only need to obtain 16 additional plans for this achievement. Your crafting table level does not matter for this achievement. You only need the plans. To check how many plans you currently have go over to your weapon stash and scroll though each weapon. If the specific weapon says Plan Yes under crafting cost, then that is one more towards the total.
Daily Challenges are by far the most straight forward way to earn crates. The challenges will reset at the same time every day so make sure that you have either completed the challenge or abandoned it. You will not get a new challenge if an old challenge is still taking up a spot. Challenges that only award food or resources won't help towards this so its up to you whether to bother with these or not. If you are struggling with a certain quest you can always have a partner help you out.
I needed to kill 5 Outlanders with a melee weapon so my buddy and I took turns killing each other in duos.
Edit: As of OCT 9th team killing no longer counts towards any daily challenges. You will be labeled a “Team killer” which is different than a “threat”.
Next up are the Supply Drops. As mentioned before, you must grab it and escape in order to get credit. The rarity of the crate can be increased for the 30 crowns and each person in the lobby has the option to do this. I have played quite a lot and have literally never seen anything higher than Purple in a solo lobby. It's going to be completely up to you whether you want to play solos or duos but I would highly suggest NOT queuing up with random teammates. You need a reliable teammate who you can trust and communicate well with in order to consistently get the crates.
Bring a fully automatic weapon and an antibiotic into the fight with 3-4 clips of ammo. Melee weapons, Pistols and Shotguns are not optimal for fighting outdoors and in open spaces. You need to be able to put bullets down range and defend yourself.
When you grab the crate hold Y to put your weapon up to run faster/longer. If you hear someone right behind you pull you weapon out and fight back. There is no sense in dying with your back turned.
Know which exit you are going to before you grab the crate. Running around aimlessly and going the wrong way will get you killed.
On Grontheim Valley, avoid the exit on the west side of the map at all costs. Taking those ladders is a death sentence.
Under this spoiler I will include a few general strategies to get the crate. Just keep in mind that none of these are foolproof and always depends on the situation.