-Finish the tutorial.

The tutorial is on the map Clear and the game opens right up to it on start up. Enter the map and follow the instructions. You can just flip through them all and not do anything, but I'd suggest actually going through it. Having a basic understanding of the controls will save you time later. Some of the more fiddly functions are a pain to use, even with a step by step guide.

-Deliver your first passenger to their destination.
This will unlock the first time a passenger is dropped off at a station. It's also the first goal for Riding The Rails, so that will unlock at the same time.

-Complete the first objective in Passenger Mode.

The first Passenger Mode level will be on the map Modern Apartment. When selected, there will be two options: Free Play & Passenger Mode. Select Passenger Mode for this. Note that older versions of the game will show the progress bar when in Free Play, but won't actually count for objective progress. The earliest versions of the game don't mention this.

The first objective will be pretty simple and the game will provide a tutorial on what it wants.

-Finish every objective in Passenger Mode.

There are two maps with Passenger Mode objectives, completing Modern Apartment will open up the mode in Bedroom. Both need to be completed for this achievement.

While I'd suggest playing normally, mostly because I find this game particularly enjoyable, there is a quick way to cheese objectives:

1. Find passengers and put down Platform.
2. Search for Starting Point in inventory.
3. Place Starting Point in front of the Platform, pointing in the correct direction.
-Note that the 'correct direction' is wherever the tail of the flag is pointing and should be placed perpendicular to the Platform.
4. Press T to enter train. Once there, press and hold T. This will relocate the train to Starting Point.
5. Some adjustments might be required, maybe even hammer Space to halt forward movement. If the train can't lineup correctly or moves off target after being relocated, this won't work.
6. Wait for the Passengers to board, then exit train mode.
7. Pull out another Starting Point and place it in front of the Station, make sure it's pointed the right direction.
8. Repeat step 4.

You can do this for every objective, but note the following:
-Two or three objectives involve business passengers, which comes with a time limit. The limit can be ignored, progress will be counted regardless.
-One task will involve making the train 'jump' for some Daredevils. The simplest way to accomplish this is pick them up and hit the gas. Falling off shelve the Platform is on counts as a 'jump'.
-As noted in step 5, sometimes some adjustments are needed. For some locations, there isn't enough space for the whole train without some support. For these instances, set some track until it's under the landing point for the train.Keep in mind that platform placement can be anywhere around the passengers. Hanging off in midair, sitting right on top of them.
-For difficult placement objectives, it's normally less trouble to complete it normally, without the cheese.

-Visit every environment.

Simply visit every map once. This has to be done in one sitting (currently) and doesn't include DLC maps. Keep in mind that visiting Clear will have to be done twice. The game normally loads right onto Clear and this, for whatever reason, doesn't count as a 'visit'.

-Ride a train off the edge of the world.

Load up any map, hold down T and wait for the achievement to pop. I would suggest Bedroom (Night) as the train will load pointing the right direction with no obstacles.

-Place 20 decorations from the spawn menu.

Load a map, open inventory and start placing items. It has to be 20 unique items, mind, not just a forest of the same tree.

-Save a file containing 100 pieces of track.

Open a map, start making wild and whacky track lines. About two complete loops around the perimeter of Bedroom should be enough.

As the achievement description says, this won't unlock until after a save.

-Ride the train around the pancakes.

Load Bedroom. Make a track that goes on top of the table just above the spawn point. Then loop the track around the pancake sitter there. One look will be enough. When done, run the train.

Interestingly, this unlocked for me when the train made a loop getting on the table, before getting close to the pancakes.

-Pull the steam whistle around the Christmas presents.

Load bedroom (Night). Build a track going around the presents under the tree. This doesn't need to be flush with the presents, so long as it's a close loop. Move the train close to one of the presents and blow the whistle.

The game notes earlier that the train has a whistle, but not how to use it. Enter the Train and click the chain, that will sound the whistle.

-Get 10 seconds of air time on the Moon.

Load Moon and build a track ramping up, up, up. 50 or so track segments should be enough. When done, hold T and wait for the achievement to pop.

-Put an alien passenger in the basket of a flying bicycle.

There's two ways to do this:
1. Hit Alt to turn on Alternative Mode, which allows item placement anywhere.
2. Open inventory, pull out bicycle and place it in the air.
3. Open inventory, pull out alien and place it in the bicycles basket.

OR

1. Lay some track in the air.
2. Put bicycle on track.
3. Put alien in basket.
4. Delete (cursor over track, press C) track beneath bike.

People have said the first way works, but it didn't for me. The second way worked, but the achievement unlocked before step 4. If one method doesn't work, try the other.

-Take an alien passenger from a crashed UFO to a station.

This takes a little setting up.

1. Make a large, circular track.
2. Wherever you like, place a platform.
3. Pull out the prop Crashed UFO and place it directly behind the platform.
4. Pull out an alien or two and drop them by the platform. They'll climb up automatically.
5. Wherever you like, place a station.
6. Get in train, pick up aliens, take them to the station. Achievement will unlock a moment or two after the aliens have entered the station.

-Recreate the moon landing shot and use the camera to take a photo.

Give yourself a bit of space for this one.
1. Pull out the Lunar Lander prop and place it wherever you like.
2. Pull out the Flag prop (there are two, either will do) and place it right by the Lunar Lander.
3. Pull out ACES Suit passengers and place two next to the flag.
4. Pull out Camera and place it in front of everything you just laid out, making sure it's pointed the correct direction.
5. Place cursor over camera (should turn into a blue dot over it) and left click.

-Put 50 unique decoration on the moon.

Same as Spruce Up The Room from the base set, but 50 this time.