I want achievements to not just be something that you see or someone else if they're interested. Maybe your best achievement is shown above your character in combat. This would mean that people could signal out better characters reasonably easy, yes it would get hectic but also there should be setting to change it (eg. only better achievements, only worse achievements, no achievements etc.)

I also had an idea that you get achievements for killing defeating enemies from different races, factions etc.

It did not cross my mind that one could in this instance have achievements for killing a certain race, should totally be in, would be a cool thing as well.

Achievement showcasing is really nice when it's mixed in with a character's profile page or inspection window.

Nice Idea, but i gotta agree with Yzaxtol, so if they would be shown on a profil page and not in Combat...it woluld be more irritating during gameplay. If you wanna check out a player and his skills/achievemnts go to his profil page. Just my two cents.

Also sounds like a good idea for recruitment in groups.
A squad leader notices that somebody has i.e. "Expert Medic"-title, and sees that he could use a medic in the group, so he brings the guy along.

I agree with both of you Yzaxtol and l1kos. I would just like a way for people to easily see your achievements without having to click links for five minutes.

I just had an idea, may not be an original one but, maybe at the victory/defeat screen there is a list of all the achievements that were got during that mission. Therefore someone looking for new team-members would just have to look at the top of the list or use a search for specific achievements.
Another idea that I had which sort of joins into the last one, is that you can get achievements multiple times. For example:
In the last battle I got say three awards one of which is 'Slay 100 Foes' (only an example). Then in the next battle I killed another 100 foes, but because I already had the achievement it didn't show up meaning a 'Squadron Leader' wouldn't see that you managed to kill 100 foes and you would miss a great opportunity.

I completely agree to this, could even perhaps be utilized in a in-depth detail level with the "home" of a player where s/he can put up trophies and similar things earned through achievements. *or which unlocked an achievement* like a Hive Tyrant head

A player could choose his favourite 3 achievements that appear on his inspection page so that he can show-off he knows his role or at least has a lot of experience playing it.

Achievements (at least the bigger ones) should give you ornaments, which you can put on your armor to show that off. But I'm quite sure this has already been discussed elsewhere.