A list of achievements that I could have earned will show up at the end of each mission. Is there a way to make it show up before each mission, so I will actively aim for them?
Yes. You absolutely can. Click on your Profile, then Achievements. Click on Swarm Campaign (assuming that's what you want) and there you will see a list of all campaign achievements arranged into sections. When you click on each individual achievement, somewhere in the description, it will tell you the name of the mission surrounded by double quotes. Achievements for the same mission are always categorised under the same section. Just find every achievement that shares the same mission name.
If you want to view the achievements while in a mission, pause the game with F10, then click on the Achievements button.
I've been told that more mission achievements are listed under the Mastery section. These are the hard mode achievements. There is a maximum of one for each mission. So if you wish to go through the game in hard mode, then it's worth checking it out before you start or while in-mission.
There is a web application for a full list of acievements. Access it here: http://sc2ach-blueplayer.rhcloud.com/
You can filter achievements by category, points and keyword.