The achievement appears to be broken in the current release (v.1.2.9). I managed to get it in v0.6.0 by using the depot method (valid according to OK-15).

Confirmation of the achievement "working" in v0.6.0

Instructions

1. Download DepotDownloader - this allows you to get old versions of Steam games
2. Extract DepotDownloader
3. Open a Powershell window and navigate to the DepotDownloader directory
4. Run the following (with your username and password): dotnet DepotDownloader.dll -app 440650 -depot 440651 -manifest 1776202259507182944 -username <username> -password <password>
5. It will now download this version of the game to a depots folder in the DepotDownloader directory
6. Copy the downloaded files and overwrite the game files where it is installed (e.g. <steam_path>\steamapps\common\Niche)
7. Backup and remove all files/folders from %USERPROFILE%\AppData\LocalLow\Team Niche before launching the game. This will force the game to regenerate the save games and achievement tracking based on this version on startup. Be sure to backup your files in case you are midway through other achievements and don't want to lose your progress
8. Launch Niche, start a new game and move to the second island. The achievement should unlock

NB: This may work on a beta version release between v0.6.0 and v1.1.0. I think the trick may be deleting your achievement progress files so they regenerate, which I didn't do with my attempts at using beta. You can try this by right-clicking the game in Steam > Properties > Betas, choose a beta in the dropdown (e.g. 1.0.4) and close the window. It will download the beta branch version. If you do try this, please let me know if it works or not and I'll update this guide accordingly 😃