Now into my first game a couple players joined and then left, so I left notes under each of the achievements I have gotten. There are three I know for a fact you can get without any other players, and a fourth that I have that I suspect you don't need anyone for. I do know that once the briefcases showed up It didn't matter that there weren't players in for most of the match. I was able to get the achievements without seeing another player. The Briefcases do not seem to spawn without another player joining. (That means that half of these achievements that I have WERE NOT attainable without that little bit of "luck" of another players joining and allowing the brief cases to spawn)
I also only played on "Two games" one of which no other players joined in on. I am also not entirely convinced that some of the achievements aren't completey busted either. I suspect you can't get any numbered (even if it is a 0/1) achievements without other players.

1
Demolition Derby
Destroy a vehicle
(I don't think you need anyone, but I could be wrong) You have to jump into the other vehicle and jump out of it for the vehicle to take damage. (I found this out after shooting a motor bike with a tank cannon 10 times and it doing no damage! After I jumped into and then out of the motorcycle it only took the tank mg and a bit of small arms fire to destroy the motorcycle.)

2
Aviator
Fly in a plane
I got this without anyone joining my game at anypoint

3
Red leader standing by
Join a team
I didn't need anyone but myself in a game.

4
Pickup a briefcase
Pickup a briefcase
You have to have at least one other player join for the brief cases to show up

5
Escape
Escape the island with all brief cases
You have to have at least one other player join for the brief cases to show up

6
Intelligence Officer
Pickup all 4 cases
You have to have at least one other player join for the brief cases to show up

7
Conscientious Objector
Win a match without killing
I was only able to get this because a couple players joined in and then left after a few minutes

8
Collecting the Toll
Complete the Intro
I was able to get this without anyone else joining in.


There might be a ninth you can get without any players joining, however I don't have it.
Evil Kenievel
Get a motocycle airborne for five seconds

Worth noting is it seems from my first try that you can't ge the achievement below (at least without there being other players in the game?)
Poke your eye out
Die from your own doing

It also seems that you couldn't the achievement for vehicle repairs either (without other people?)
Vehicle Repair
Repair 25 vehicle parts

Also I couldn't seem to get the tires to pop on any vehicle, meaning that it doesn't seem likely you can get this achievement either.
Pop goes the Weasel
Pop 25 tires

I think it probably goes without saying that without other players you can't get any of the teammate or enemy kill related achievements. (I suspect any numbered achievement you can't get without other players.)
And there you go! My first guide. Let me know how I can improve. Have a good day!