On A Rail - Travel by minecart at least 1 km from where you started:
What might be implied:
- You must be in a minecart for the entire time
- You might need to be on rails for the entire time?

1) Use boats to reach 1k distance (easy, not faster than minecarts until 1.7 boats, unsure if it works in 1.7+)
Issues:
- A boat is not a minecart, achievement implies you need to be in a minecart for the entire time
- Not on rails for the entire time

2) Minecart boosting (only faster on top of the nether), faster RSG, variable SSG
Issues:
- Is Minecart boosting allowed? Crafterdark's SSG route suggests yes.
- Is Nether Roof allowed (i.e. y>=128 in nether dimension)?
- If Nether Roof is allowed, what methods are allowed to be used to get onto the Nether Roof?
- Not on rails for the entire time

3) Minecart boosting with leaf bridge (faster than flying machine according to matthew)
Issues:
- Is Minecart boosting allowed? Crafterdark's SSG route suggests yes.
- Not on rails for the entire time

4) Fastest End gateway warp (1.9+ only and probably unbeatable fastest method)
Issues:
- If the chunk isn't loaded before travelling through an end gateway with a minecart, upon travelling through, the player exists in a glitched intermediate state, suggesting that travelling through an end gateway with a minecart was not meant to be allowed, but happens to work anyway
- Not on rails for the entire time

5) Flying machine (faster? slower?)
Issues:
- On a rail for the entire time, but it's a single rail that's being pushed

6) Normal 1k rails method on nether roof (saves time from mining, only relevant if somehow minecart boosting is banned but nether roof is allowed)
Issues:
- Is Nether Roof allowed (i.e. y>=128 in nether dimension)?
- If Nether Roof is allowed, what methods are allowed to be used to get onto the Nether Roof?

7) Normal 1k rails method OR minecart boosting after building/digging 1k blocks (slowest either way)
Issues:
- None, but slowest method