You can get this achievement at the first mission with the Flak gun, just blow everything up.
when you didn´t get the achievement, reload checkpoint.
Also you can do it the third (3) story mission.
The Mission is about, to find Sheldon in the jungle but before you have to find pang who is going to be killed because he lost to much money in the game room ( ^^ ).
After you save him and get the file for your PDA you are going to the new marked place.
A Cutscene with Sheldon appears then soldiers coming up and you grab the minigun and fire.
Here you can do the 30 Objekts in 60 seconds achievement, you only need to shot the enemies and the old stones around you.
And when you didn´t got it, just reload the checkpoint and try again.
Here you can also do the kill 20 enemies in 60 seconds achievement.
All you have to do is follow Shelon and kill the soldiers.
Again, when you didn´t got, reload checkpoint and try again.