Practically Unmissable:

• Donkey - Use the Donkey at the start of the game
  
• Map - Use the Map to move between areas
  
• Borrowing Groceries - Tell Bobby that his mother wants thread, then take sugar, coffee, biscuits and carrots
  
• Trolley - Fix trolley with screw and use it
  
• Looks Rude - Look and Talk to Swappy outside Saloon
  
• Explorer - Discover all the places in the map.
  
• Peace Pipe - Smoke Peace Pipe with Chief after swapping out tobacco from inventory
  
• Costume - Change into Father Anselmo's cassock at bank
  
• Explosion - Blow up Bank
  
• Skull - Get the skull from Sam after rescuing him from the well
  
• Jail - Get thrown in jail for cheating at poker
  
• Under Attack - Fort Apache attacked by actual Apaches
  
• 3 Skulls of the Toltecs - Finish the game.

These last three are potentially missable, but highly achieveable by talking to every character and picking everything up as gamers tend to do. But just to be extra clear:

All Items - Pick all the items up.
Picket, Pick, Cassock, Tobacco, Screw, Sign, Logs, Cigar, $40, Empty Whiskey Bottle, Sugar, Biscuits, Coffee, Carrots, Coffee Pot, Knife, Candle, Magic Cloud bottle, Matches, Rope, Parrot, Fabric, Gum, Fishing Rod, Horn, Tabasco Sauce, Union Flag, Dynamite, Barley Seeds, Barley, Dirty French Uniform, Sponge, Bowl of Rice, Clean French Uniform, Full Whiskey bottle, Fixed balloon, Gunbelt, Ticket, Bucket, Gold Skull, Stethoscope, Pillow 1, Pillow 2, Fake $100 Bill, Donkey's Hat, Cards, $10, Book, Jail key, Medal, Corkscrew, Ball, Green Book, Oracle Key

Win at Poker - No cheaters allowed. - Win a hand normally

Chatterbox - Talk to all the characters.

• Buck - Start of Game
  
• Friar Bacon - Start of Game
  
• French Soldier - Outside Monastery
  
• Jon Nodoffsky (Sleeping Mexican) - Outside Monastery
  
• General Lardbelly (Friar Bacon)
  
• Sam (bottom of the well)
  
• Telegraphist
  
• Shopkeeper Bobby - General Store
  
• Deputy Pettyboom - Jail
  
• Bank Cashier - Bank
  
• Mimi - Saloon Balcony
  
• Swappy Smith - Layabout outside saloon
  
• Drunkard - Saloon
  
• Sheriff - Saloon
  
• Thug at Bar - Saloon
  
• Barman - Saloon
  
• Dancer - Saloon (upstairs)
  
• Old Lady in rocking chair
  
• Parish Priest - in Church
  
• Apache by totem pole
  
• Apache by tent
  
• Apache Security Officer
  
• Parrot - Cemetery
  
• Tom - Distillery in Forest
  
• Train Engineer - Fort Apache
  
• Lieutenant - Fort Apache
  
• Troops - Fort Apache
  
• Lookout - Fort Apache
  
• Colonel Leconte - Fort Apache / Saloon
  
• Apache Chief - Indian Village
  
• Graduate Bull (Interpreter) - Indian Village / Fort Apache Jail
  
• Senator - Indian Village
  
• Witch Doctor - Indian Village*
  
• Jail Warden - Fort Apache
  
• Wun Hung Lo - Fort Apache
  
• Sergeant Smith - Fort Apache
  
• Anti-Alcohol Ladies - Fort Apache
  
• Dickson - Saloon / Jail
  
• Provisional Revolutionary Leader - Hideout
  
• Father Anselmo - Fort Apache Jail -- achievement should pop here, but if not talk at Saloon later

*Talk to the Chief when Graduate Bull is in the jail and choose option [A], which will make the Witch Doctor talk.