Killed a Constructor without it ever building another bot
The earliest time you'll come across a Construct is during the side quest "Out of Body Experience". These guys are pretty tough and you may have a few issues in your earlier levels trying to bring one down at your current level and weapons to hand.
There's a little trick though. Once you've come face to face with one, kill all the initial enemies around him and then die. Once you respawn around the corner, the Construct will no longer build anymore robots. This now gives you the time to kill him without the worry of more enemies being spawned by him and missing out on the achievement.
I leveled up to 23 then completed the mission mentioned by #1. The constructor was lv 14. Just wasted it with a corrosive submachine gun. @#2, the first objective is on top of Bloodshot Stronghold. Continue past the circular area that looks like a whirlpool and you'll eventually exit the Stronghold into the Bloodshot Ramparts. A marker should take you there once you're in the Ramparts.
I tried the 'out of body' quest on level 14 siren and was having a lot of trouble with it. The Constructor was launching non-stop missiles and had a fire-radius attack if you got too close. Solved it by hiding behind the toll booth on the nearby road. He'll continue shooting rockets but they won't hit you through the windows, you can pick him off at will then.