There are no missable achievements.
The game have a lot of checkpoint. So just do the game normaly and then come check the achievement you miss.

You got a friend in me: Catch the first chick and take it with you
Load Checkpoint 2, run to the chick, catch it and don't move till the achievement pop (1 min)

For the greater good: Use the tiny chick to solve the hammer puzzle
Load Checkpoint 4, solve the puzzle using the chick

Yes, I deserve it!: Use ravengirl to solve the hammer puzzle.
Load checkpoint 4, solve the puzzle using yourself (it will not kill you)

I went train spotting: Survive the train rides without dying.
Load Ceckpoint 6, don't die till the end with the wolf head

Someone bawked!: Survive the Coocoo House without ever getting caught.
Load Checkpoint 7 and run wihtout dying until the achievement pop

You went too far: "Use" all the possible chicks for the Battery Maker 2000.
Load Checkpoint 9 run to the wall on the left then go back and pull the lever. It should grab all of them for the battery

Chick magnet: Have 20 chicks cling to you as a shield
Load Checkpoint 9 jump over the wall with the battery you made with the previous achievement and gather 20 chicks

I will follow you: Lure 80 chicks into the bowels of the muncher
Load checkpoint 9, go to the grinder at the end and grab the hook above the grinder

Join the circus: Survive the Funworld Trials without dying.
Load checkpoint 12, don't die till it pop

Lord of the Birds: Survive the Tintown Trials without dying.
Load checkpoint 14, don't die till the end of the chapter (starting from checkpoint 15 doesn't work)

That's unfortunate!: Die in every possible way
I hope I don't miss some:
- Fall damage
- Jump in a pit
- Hit by a train
- Crunch by spike door (checkpoint 5)
- Grinder (checkpoint 9 with the hook above)
- Saw (checkpoint 12)
- Hand Crunch (checkpoint 12)
- Fire (checkpoint 12)
- Getting bonk during the trial chapter 14-15