This can easily be done during the very first section of the campaign during Chapter 1: The Museum of Military Glory, Section 1: Old Town.
You'll start off with some story, and come to a burning tree and encounter your first enemies. Use the chainsaw to kill 3 of them in a row to unlock Lumberjack - Chainsawed 3 opponents or enemies in a row.
Now, continue to move through the mission, making sure to trigger the declassified mission as well. During the next section, you'll want to run through as much as possible until you see an E-Hole open up in front of you. As it opens, and enemies begin to come out, throw a frag grenade into the hole to get: Plug That Hole - Closed an E-Hole with explosives and Clusterluck - Killed multiple opponents or enemies with one grenade. You should have now unlocked the achievement.
If you were unsuccessful, you can restart your last checkpoint or get 3 headshots in a row to get: Hat Trick - Scored 3 headshots in a row without dying.
Note: The achievement will unlock in-game, and you are free to restart checkpoints.