If you want to get all the previous achievements, here's a good guide:

https://psteamcommunity.yuanyoumao.com/sharedfiles/filedetails/?id=2866546592

Right now, some previous achievements might be harder to do, since new stuff has been added. However, this is not in the scope of this guide.

30.09.2024 EDIT:
Recently, a new guide has popped up, which aims to be a centre for all basic information on Necesse. Currently, the maker of the guide is just a few achievements short of 100%. If you need help with older achievements, or lack fundamental knowledge about the game, feel free to check the guide out!

https://psteamcommunity.yuanyoumao.com/sharedfiles/filedetails/?id=3337827224

In the meantime, since most of the achievements not yet earned by the guide maker are the recently added ones (6/8), feel free to read ahead for information on how to get them.

The 16 new achievements are straightforward and require time more than effort. As long as you keep the information contained in this guide in mind, you will get the achievements in no time.

1. Adventure Begins - Accept your first quest from the Elder. - Just go to the Elder and grab a quest.

2. Feeling Stylish - Get a new look from the Stylist - a simple haircut will do. While you're here, buy the two blazers and two pairs of dress shoes for another achievement.

3. Teamwork - Have a settler join your adventure party - You can achieve this by speaking with them and getting them to follow you, or pressing the 'C' button and giving them an order to follow you.

4. Secret Service - Have only 2 guards in your adventure party, both wearing sunglasses, blazer and dress shoes - the blazers and dress shoes you bought from the Stylist are required for this achievement. The sunglasses can be bought from the Travelling Merchant.

5. Safety Last - Take damage from a bundle of TNT - you can either rig up a bundle of dynamite to a lever yourself using wire, or you can use an existing bundle of TNT from a cave.

6. Demolition Expert - Kill an enemy with a bomb - use a bomb to kill an enemy.

7. Hot Tub - Swim in lava while under the effect of fire resistance - fire resistance can be obtained from a fire resistance potion.

8. Home Alone - Kill a raider with a trap - rig up some traps (usually found underground), and use them during a raid to kill a raider. It's best to first bring them down to low HP using another weapon, since traps do so little damage.

9. Dodge This! - Defeat the Fallen Wizard while 5 Fallen Dragons are alive - this achievement can be pretty tough; you can come back to it after doing incursions and getting better gear, however it is still doable with previous patch endgame gear.

10. Wardrobe on the go! - Get access to 4 item sets - The Fallen Wizard drops an item, which gives you access to the 4 item sets, which this achievement requires.

11. Take it to the next level - Complete an incursion - You need to complete an incursion, for which you need a Gateway Tablet and a Fallen Altar. The tablet you get from defeating the Fallen Wizard; it's required to craft a Fallen Altar. When you use the tablet in the altar, you need to complete an objective and fight the boss. After defeating the boss, the incursion is complete!

12. Master of Sun and Moon - Defeat Sunlight Champion and Moonlight Dancer at Tier 5 or higher - there are Sun Arena and Moon Arena tablets, which allow you to defeat Sunlight Champion and Moonlight Dancer respectively. In order to get this achievement, you need to defeat them both at Tier 5 or higher.

13. Empowered - Upgrade and equip a full set of Tier 5 armor - self-explanatory; you can upgrade armor in the Upgrade Station using Upgrade Shards; the Station is made in the Fallen Workstation.

14. Crystallized - Reach the full potential of the Ruby or Amethyst set - The Ruby / Amethyst sets are made in the Fallen Workstation from Omnicrystals, Pearlescent Diamonds and Rubies or Amethysts and consist of:
- Ruby Crown or Amethyst Helmet
- Crystal Chestplate
- Crystal Boots

Pearlescent Diamonds are obtained from Crystal Hollow Extraction Incursions, while Omnicrystals are obtained from Crystal Hollow Hunt Incursions.

I would recommend doing the Amethyst set, rather than the Ruby set; the Amethyst Helmet gives you additional resilience, thus making the achievement easier to get.

The following information is taken from this source: Dude's post on TrueSteamAchievements[truesteamachievements.com]

In order to reach the full potential, you need 400 resilience. For that you will need:
- Manica (made from Chain Shirt and Vambrace in Advanced Workstation)
- Clockwork Heart (made in Fallen Workstation) [Your health needs to be maxed out with Life Elixirs to 300 base health]
- Frozen Soul [Which will give you 25 resilience when combined with Clockwork Heart] [35 with Tough enchantment]
- Clay Gauntlet
You will still need to enchant several items with the Tough enchantment; do so first on the armour, if it's Tier 5 it will give +20 resilience instead of +10.

Alternatively, as long as you have Clockwork Heart, you can eat food which gives you additional Max Health to convert into resilience. For instance, Pork Tenderloin gives you +80 max health, which translates into +40 resilience.

15. You and what Army? Have 10 settlers in your adventure party with full Tier 5 armor and weapon - it's pretty easy to get the armour, some incursions will give entire sets of Tier 5 armor on their own; the weapons are trickier, since most of them cannot be used by your settlers.

16. Me and this Army! - Defeat an incursion boss with only damage from settlers - With 10 settlers having Tier 5 weapons and armour, it's really easy - just get a Tier 1 incursion against a Reaper (Forest Deep Cave Incursion Tier 1) and you're golden. Remember to give your party as many potions as you can; that way you ensure they won't die. Apparently, settlers are not affected by banners, but I'd advise you to set them up just in case.

There you have it! That's all the new achievements you can get in Necesse as of version 0.26.0
All I've said should also apply to 0.30.0, please leave a comment if something is out of date and should be corrected.

Hopefully you found the information in this guide useful.