Although there are many methods used to get the portal kill achievement, here is the one I used, and it works.

You can do this on any Arena mode with a map where it is possible to put a portal out of bounds. (I recommend the Team Deathmatch queue, long games, short queue times, no objective.)

First, you need to put your first portal in the area that is off the map (like the death chamber or little wall off the map).

Next, find and enemy and engage in combat with them close to a portal wall. Once they are engaged, put down your second portal on the portal wall and go through it. If all goes according to plan, they will follow you.

This next part gets a little bit inconsistent. Sometimes you get kill credit after you've died, sometimes you don't. When I got the achievement, it was after I died, but this will probably take a few attempts to work. (You also need to make sure no other teammate shoots them, otherwise they will get credit and not you.)

Try to stay alive after going through the portal as long as possible just to be safe, but hopefully, if the enemy follows you, they will die and you will get the kill credit and the achievement for getting a portal kill. (If it doesn't pop immediately, don't worry. It took a couple seconds for me.)

For the subsequent portal trophies, you must simply follow this process as many times as needed until you get the achievement.

I hope you all enjoyed this guide!