To start with I would suggest entering the commands to enable certain traits, this can be done by pressing RT,LT,RB & LB at the same time then entering in the following:
These don't disable achievements, so I would highly recommend them.
The Painter career requires 2 skills, painting and either charisma or logic, depending on which path you have chosen. Now you could power train them before you start work or just train up in between your work shifts, entirely up to you.
For each promotion their will be a skill level requirement and also a daily task to improve your job performance. The daily task is to paint paintings and still remains the same task regardless of which path you chose.
The patron of the arts path requires charisma whilst the master of the real requires logic. As previously mentioned there isn't a massive difference between the two, both being quite simple, so choice is up to you.
Optionally I found having sims energized and focused helped with job promotions, so drink some coffee and play a bit of chess before going to work if you wish.
Once you have gained the final promotion you will gain the achievement.
As a side note, in regards to any Sims 4 achievements not unlocking, I have found a solution that I had to use a few times. To unlock anything follow the steps below:
Remove profile from Xbox.
Reset Xbox via settings.
Load up the save in which you have earned the achievement but it has not unlocked.
It should pop before it finishes loading.