There are no missable achievements in Deliver At All Costs. You can replay missions and roam the map after completing the game.
Story-based

Out Of The Frying Pan…
Future In Your Hands
That Settles It…
Auto Rescue
Cartophile
This will pop when you start the final mission.
The Final Curtain Call
Collectathon
Crate Expectations 1
See Crate Expectations 4.
Crate Expectations 2
See Crate Expectations 4.
Crate Expectations 3
See Crate Expectations 4.
Crate Expectations 4
Money crates are scattered throughout the map. You can collect 250 within the first map (Act I) if you’re thorough. Their value increases in Acts II and III.
Scallywag
See Buccaneer Extraordinaire.
Buccaneer Extraordinaire
Hidden chests are red, sparkly chests stashed in out-of-the-way places. They contain parts to upgrade the company car.
To-Do List
Bumper Blunder
You’ll get this achievement naturally. Just drive it like you stole it.
Divebomb Delivery
If you don’t get this achievement naturally, Mt. Calahan is a great place to go cliff diving.
Do-Good Delivery Driver
Encounters are represented by a green question mark on the map. There are 10 of them:
- Mr. Palmer & The Giant Worms (Solution: Climb to the roof across the yard from your apartment in The Steps.)
- The Mayor’s Doppelganger (Solution: Look for him just southwest of We Deliver in St. Monique City.)
- The Lost Mascot (Solution: Solve the puzzle by pushing crates on the cargo ship in Port Belle.)
- Cash & Burn (Solution: Collect 200 money crates for Hawkeye in the southeast corner of Old Monique. This earns you the Mysterious Key for free if you don’t want to buy it from the shop.)
- The Search For The Sombrero (Solution: Look for him on the bridge under construction in Reefside.)
- Save Mother Nature (Solution: Sneak into the work site to the west and open the valve.)
- Bringing Back The Tunes (Solution: Buy the gramophone for her at a shop. Note: You can equip the gramophone from your inventory to get an old-time soundtrack, even after you give it to Ms. Granger!)
- Race Down The Mountain (Solution: Race down that mountain!)
- Bubble & The Ghost Car (Solution: Drive the ghost car all the way to the volcano at the center of Mt. Calahan and double click the exit car button to send it to its doom.)
- Dirt Devils (Solution: Race around that track!)
Ultra Rapid Rally Driver
Keep collecting parts and blueprints and you’ll get this upgrade eventually. It comes in handy for the final mission.
Ragdoll Rodeo
You’ll probably get this achievement naturally. Every time you have to climb for a collectable, just take the shortcut back down to the ground by jumping.
Dough Collector
I saved until I had 10,000 and then spent it all at once to get the next achievement. I don’t know if it’s necessary to do that or if it’s cumulative.
Big Shot
Go on a shopping spree at one of the stores marked with a briefcase full of money on the map.
Gadget Gandhi
You should get all these naturally if you keep finding/buying blueprints and spare parts. A Gandhi reference in regard to gadgets makes about as much sense as anything else in this game, I guess. The final upgrade is story-based.
Blame The World
While on foot, press the kick button (LB for me) to take out your frustration on smaller physics-based objects in the game world.
Meatbag Maneuvering
While on foot, press the shove button (RB for me) to take out your frustration on NPCs in the game world.
Under The Wire
I found the easiest way to get this was by replaying the Fire Sale mission (as if you didn’t have to do that one enough times already; see Flawless Victory below). Before turning in your final crate(s) of fliers/flyers, get near the fire and wait for the timer to reach 0 before accelerating toward it. (If it doesn’t unlock you might have actually finished too early; go on 0, not on 1!)
Duct Tape Engineer
I found the easiest way to get this was by replaying the Shake, Rattle and Explode mission. Run over the fireworks that get stuck on the ground to knock your wheels off. Then hop out and repair them (after getting a shove from an unhappy citizen or two).
Mission-based

Drive just crazy enough to drop the maximum number of melons you can get away with losing at the beginning of the mission and after the melons are “cleaned.” If you drop them all, you’ll fail.
Melon Juggling Master
Drive like you’re driving Miss Daisy. Be very careful to re-collect as many melons as the game will give you after they’re “cleaned” (i.e., don’t drive away too soon).
Melon Melancholy
Just load the melons and then immediately do an evasive maneuver (i.e., cheerio, sudden acceleration-and-brake test, etc.).
Blue Beast Ballistics
After loading the marlin in the company car, there’s a spot nearby where you can crash into the end of the pier or slam on the brakes and send the fish flying back into the sea.
Flawless Victory
You have to complete all three phases of the mission without a failure. No starting over from a checkpoint. This may take a few tries but it definitely gets easier.
Box Office Hit
You have to carefully collect seven crates of fliers/flyers at once. I found this to be easier than the previous achievement.
Ruthless Competition
I found this achievement to be really fun. Your first priority is to disable the competitor’s courier car and get the package from them. Once that’s done, you have all the time you want to ram the other competitor vehicles or just watch them crash themselves into things. If you have the Wheel Spikes upgrade, this is a great time to equip it!
A Warm Farewell
You have to get to Norman and talk to him first, then the rest is self-explanatory.
Pop Goes The Tire
This one is relatively easy. When you’re in control of the RC cars, just target other vehicles’ tires. They pop right off. You can do 24 of them with the first RC car, before the police RC cars are sent in.
Bullseye Bailout
Some people said they had trouble with this one but I got it first try. Just drive very slowly and carefully when the cargo starts malfunctioning. There’s no time limit until the very end, when you should have just enough time to get to the destination and press the catapult button.
Self-Destruction Derby
Don’t attach the ball to your company car with the winch, just crash into it a lot until you blow up.
Trailblazer
This is a lot like Tron light cycles or that snake game. Just keep driving around in big circles without overlapping your trail until the achievement pops.
Shadow Mechanic
I got this one first try even though Gordon saw me and yelled at me at one point. So, I’m not sure what detection means here, but just try to be sneaky. It’s not that hard.
Barrel Bolter
This is the big one. 25+ attempts seems to be the norm from most people, including yours truly. I found the most important thing to be equipping the Time Control upgrade and using it A LOT. If you hit a rolling OR stationary barrel, you have to abort the mission and replay from the beginning (but it helps to play through the mission several “no-pressure” times to memorize the tricky spots before you start aborting repeatedly). There are a couple of checkpoints, so if you die mid-run from anything that ISN’T A BARREL, you can keep playing from the last checkpoint and hope for a lucky finish.