Assassin's Creed Valhalla

What this achievement actually requires you to do is to progress through and beat the boss at the end of the third region all without using a single elk shrine on that run. While you can't use any elk shrines on this run, you CAN buy elk antlers from the coin merchants to heal that way. Buying those will not void this achievement.

Before attempting this achievement, there are a few things you should do to prepare to make this easier, as this can be one of the harder achievements in this DLC:
 

• Complete the side quest in Kaldstad discussed in Freedom Fighter (40G) since this grants you a free revive once per run. This makes this achievement far more manageable and less stressful.
• Consider obtaining and fully upgrading the Dwarven Defender Outfit. This outfit is located in Dokkerland. Head all the way down to the bottom of the region, keeping an eye on the mountain with lava flowing down it off to the left a bit. Once you get to the base of this mountain near the end of this region, follow the obvious path up the mountain around the lava, and you'll eventually reach a glowing chest you can't open. Head past it and up further on the mountain until you reach a stone archway. Head through it and jump down into the hay behind the chest. This allows you to open it and obtain the outfit. Now, if you collect enough Thoughts from beating bosses, you can fully upgrade it. Its fourth and fifth upgrades give you passive healing abilities that will make this achievement easier. I will mention here though that I did this achievement without using this outfit, in case you don't want to amass and spend over 50 Thoughts on fully upgrading this outfit before you attempt this achievement.
• Consider buying the Nar Favor that reduces costs of coin merchants by 30%. This will give you more opportunities to buy health, health upgrades, weapon upgrades, and runes from coin merchants, making you more likely to succeed in this run.

With that all done (or as much as you prefer), you're ready to start this run. Your biggest asset for success here is going to be taking advantage of the save exploit to ensure you reload in case you really mess up and take a lot of damage and/or die. Here is how the exploit works:

The game autosaves right after you complete every encounter in this DLC, as well as right before every boss fight. What this means is that you can quit out and reload your save whenever you feel like you really screwed up, took too much damage, or even died. For example, you're having a great run and then those druid enemies in Nidheim really destroy your health with their fire attacks after you screwed up some assassinations. Rather than being stuck with the results of that fight (such as all the health you lost), you can pause and quit to the main menu, then continue your game. You'll be back to just before you started that encounter, allowing you to reattempt it again, hopefully with better results. You can use this during any encounter or boss fight to ensure things go better for you, or just that you succeed and don't die.

There's no need to be so conservative that you're reloading your save every time you get hit. Personally, I would only allow myself a maximum of two hits per regular encounter before I'd reload. The first and second boss fights have a little more leeway since you can heal at the coin merchant right before each one, so you should be able to go into each boss fight with full health (or close enough). Then, in Nidheim, I highly recommend just avoiding almost every encounter. The druids are so overpowered that it isn't worth the stress. Only do encounters with enemies already spawned, and only if you either need the coins to buy antlers or if the reward will upgrade your weapon (first priority) or health (second priority). You should therefore be able to go into the Nidhogg fight with full health or close to it, and definitely your revive still left. This should give you plenty of margin for error during this boss fight. As soon as you beat the dragon, you'll unlock this achievement.

Those are really the main tips unique for this achievement. I also recommend reading through my tips in The Queen's Fall (20G), as they all apply to this run as well.