As of this moment, there are five apps for Android that allow one to work on their MyAnimeList profile. Of those five, only one works.
This post has a lot of images, so I am cutting it short here.
Currently, the only one that works. It is, honestly, the best looking one, too. This worked for me for awhile, but then it stopped working, which caused me to switch for MAL for Android 2.
Atarashii! is the best one in terms of presentation.
It actually gives you an option to change it, too.
You can select which parts of your list you want to display.
There are a couple shortcomings, though.
First, it does not provide enough information about a series. All it provides for a show is the synopsis, MAL stats (which are media type, e.g. TV, OVA, and media status, i.e. airing or not airing), status (i.e., watching, dropped, on hold, etc.), progress, and rating (personal and site-wide). It does not provide any sequels, prequels, summaries, or side stories, which I find incredibly convenient.
Second, the search function is limited. It can search through your own list, but it cannot search throughout the MAL database. In other words, if it is not already on your list, then it will not show up in the search results. Lame.
As this is the only one that works right now, I can only recommend this one.
MAL for Android 2
My preferred option, but with one shortcoming: it stopped working. It is not as pretty as Atarashii!, but it does not have the two shortcomings of Atarashii!.
It does not work anymore, but I will go back to it once it does.
Momo MAL Client II
Does not work. I could not even log in. This is the only one with a nice log in page; it would be neat if it allowed users to change the image.
Does not work, but the ads do work. This is the only that uses ads, as far as I know, so I think that will put some people off. From the screenshots on the Playstore, it does not look too bad. I do not like ads, though.
Does not work. There is a PRO version, but I did not try it.