For the most part I used the guide from F1 2010, but I wanted to add everything I know to make it easy. Here we go....
PLAYING ON HARD
If your going to try this on hard without switching assists, there's not much I can do to help besides telling you to know the tracks well and be able to manually shift. Plus, qualifying is very important.
If your starting a new career, I would suggest selecting Williams as your team.
If your at the beginning of a new season with a better team, like Red Bull or Ferrari, even better.
Go to my F1 and turn autosave off and then manually save it to make sure it doesn't come back on if you reloaded before saving. VulturousPiano and RaucousRichard confirmed that autosave DOES NOT have to be off.
When at the calendar, select the difficulty to Hard, race weekend to short, and distance three laps.
Skip practice unless you want to try it out, but I'd suggest going to qualifying.
For qualifying (and practice if your doing it) pause the game when they give you control of the car and switch manual to automatic, turn the suggested line on to always, and traction from medium to full. Keep auto brake off for now. Go ahead and qualify, by running decent laps and never going off track, I almost always managed to get 18th. There was usually a three to four second gap from 17th to 18th. If for some reason you have to go back to the garage or your satisfied with your time, pause the game and switch everything back until it says hard instead of custom. (a few times I forgot to do this but I still managed to get the achievement, so I'm not positive if you have to switch it back, but I did it to be safe). On to the race....
Again, once you get control of the car switch the same things that you did before. Now here's the most important part to winning the races, most tracks have a sharp turn at the beginning, so your going to want to try and get to at least the top 5 by charging through the field and braking late, hoping to bank off someone with out destroying your wing or getting a penalty and hope for another turn shortly or else they will get away. Also, I used KERS at the beginning to get more positions. Only twice did I get it on my first try, so it will take practice. (remember to switch everything back before restarting). Some tracks I knew I wouldn't win, so I was happy with a top five. Once your happy where you are settled, turn auto brake on and block as best that you can. (remember that you have two rewinds if someone gets by or you get a penalty). If you know the track well and feel comfortable without it, this isn't necessary, I just did it to prevent any slip ups and wasting my rewinds.
Before you cross the line on lap three, switch everything back so it says hard instead of custom and manually save it after the race if your happy with your result. (I forgot to do this once and dashboarded it before I got back to the menu just to be safe even though I had auto save off).
Overall it wasn't bad, I'm not sure how tough it will be with Williams, but I found it not too challenging with Red Bull. I won the championship on the fourth of last race and found that usually one or two guys will always win when you don't, so wrecking them and still winning without a penalty helps a ton. I would suggest focusing on winning though unless your only a few points away from clinching and want to get it over with quicker.
If you can shift well and know the tracks, you may be able to do hard without switching the assists.
Vytenis on x360a mentioned that the assist switching works as well, but I thought I'd put everything I know :)
If you still need help, leave a comment or PM me and I'll get back to you as soon as possible.