Danke! Hat ohne Probleme funktioniert (nachdem ich 5x gecheckt habe, welche Fahrzeuge ich in der Liste vergessen hatte). Ich finde trotzdem die Achievement-Beschreibung sehr irreführend.

It worked for me, without using mods, small map x4 time scale and x3 time forward starting 1950. I didn't replace any of my vehicles, but I set the maintenance to150%

CLOSE the official script mod "Legacy Vehicle"(If you have installed the Deluxe DLC, the mod can not be closed actually, so remember uninstall dlc) and "Deluxe Content"

Got this achievement today editing the *.lua file as described below.

I did NOT manage to achieve this using
* Normal playthrough...
* Using "Achievements with mods" mod - although this was working with other achievements

I had to do the following
* Edit basic_config.lua file as described below
* Start Free game with Sandbox mode (Urban games owned mod) enabled and i.e. NOT using "Achievements with mods" mod
* Create a basic road, two bus stops, line, and road depot
* Buy first vehicle (Stagecoach (1850)) and leave it in the depot
* Jump (Sandbox mode ability) to date 1869-12-25, wait 5 days till 1870-01-01, purchase next vehicle (L'Obeissante (1870)) and leave it in the depot
* Iterate date jumping for other vehicles based on vehicle list and leave them in the depot
* Reach year 2020, put all 16 vehicles on the line, achievement unlocked immediately

I did this for the european vehicle set / map setting, without Deluxe Edition.

Sad, that it only works this way, but it did.

Followed the rules from comment below and finally got it, thanks :)

"
Found a solution to get this very fast:
Go into your TPF2 root folder under \SteamLibrary\steamapps\common\Transport Fever 2\res\config

Open the "base_config.lua" file with NotePad++ or Editor and search with CTRL-F for "Achievements" and you will find the following line : "game.config.earnAchievementsWithMods = false" and correct it to "true", then save the file. Double check if it truly changed.
Should look like then:
game.config.earnAchievementsWithMods = true

Load a save game with just Sandbox Mode as a mod (to save you some time :))

Construct a line and a depot and circle through the years making sure to get all 16 separate vehicles in your depot. Don't put them on a line yet.

After you've gathered all the vehicles put them on a line and you should get the achievement.
"

https://www.transportfever.net/thread/14979-museum-line-achievement/?postID=303878#post303878

Found a solution to get this very fast:
Go into your TPF2 root folder under \SteamLibrary\steamapps\common\Transport Fever 2\res\config

Open the "base_config.lua" file with NotePad++ or Editor and search with CTRL-F for "Achievements" and you will find the following line : "game.config.earnAchievementsWithMods = false" and correct it to "true", then save the file. Double check if it truly changed.
Should look like then:
game.config.earnAchievementsWithMods = true

Load a save game with just Sandbox Mode as a mod (to save you some time :))

Construct a line and a depot and circle through the years making sure to get all 16 separate vehicles in your depot. Don't put them on a line yet.

After you've gathered all the vehicles put them on a line and you should get the achievement.

Yipee! Just got the achievement - was my last one. ;o)
* config to still allow mods and experimental maps - but have not used any this time.
* Never changed the speed, and again normal difficulty.
* This time I bought each vehicle itself without cloning or replacing.
Started with one long line of oil across the map to provide the money, and after that more or less afked/watched youtube and just bought the new vehicles when possible.

Just did another run, and again nothing. :-(
* Again with mods, but with changed config.
* This time I never changed the speed from 1x
* This time I used difficulity Normal instead of Easy
* Again 1:5 and Very Large Map.
* But looking at my line in 2019 i realized that the age of the vehicles are not matching, and I think this is because I used clone & replace instead of buying them new - which for now is in my opinion the most probable reason it has not worked again.

It hasn't worked for me :-(
* I have used mods, but i changed the config so that I can get achievements for mods, and for many others it worked without a problem.
* I run this game with 4x speed, which I think is the most probable reason it has not worked...
* I think I also did my run with experimental map size (1:5 and larger size - about 7,2x36km), so this can also be an issue...

It's not working for me