One simple request. Make achievements looks like actual achievements. Explanation: Makes them pop in the middle of your screen with a nice frame and maybe a visual effect(blood on the sides of the screen or something). Dont just make them appear on a corner that noone notice them.
Also a fully customized UI would be nice (something like Rift online or bartender addon).

I also like it when the Achievement pops up in front of your screen a visual effect would be cool depending on the achievement, As for the UI - They already said over here that you will be able to customize the UI

I'd rather have it in the corner. The last thing I want is an achievement window blocking my ranged shots

But there could be other on screen indicators to direct your attention there. The window doesn't necessarily need to be in the middle of the screen to get your attention. There are many ways to light up the UI so you know something substantial has happened, and then you're bound to notice the box, wherever it may be.

Yes - there will be an animation in front of your screen when you get Achievements and such things but... you'll be able to turn them off and keep only the corner notifications. Is this okay with you guys?

Could we also get a button, something small that blinks in the corner, even after the achievement disappeared, so we can look up what we did there?

It will probably be like this, yes. Still not sure about a button on screen since we probably won't have a Mouse Cursor while playing. There will be a way to see the details of the recent things you have accomplished and links to the proper interfaces. I'll find something neat, I promise (if not, well, you can scream at me during closed beta )

You mean a small square with a honeycomb in it?

I want achievements to actually unlock armor or banners this way they will mean something. Imagine carrying a banner on your backpack for unlocking a crazy hard achievement. Or maybe even something small like a purity seal/spirit stone. Maybe even something in your personal quarters.

Are achievements going to be for stupid stuff like completing a tutorial? or will they be legitimate achievements?

Yes, that kind of things. Achievements will be meaningful and have proper rewards attached to them. There will be different types of achievements so expect different types of rewards, small and big.