This is copied over from my TrueAchievements (Xbox) solution. Yes, I have this achievement on my Xbox account, just not on Steam.
You can reach level 50 quicker with the following ways (that still work in the latest patch):
Pickpocket: If you pickpocket everyone everywhere to get your skill up to 100. This should get you 10 levels or so. Make sure you save often to ensure if discovered you can reload an earlier save. Or, you can have a tutor teach you a skill and pickpocket the money back, however it becomes inefficient (explained later in guide).
Magic: You can self cast spells to increase their skill rapidly. Note that Destruction spells are excluded from this. A very good way to do this is to cast a healing spell while you cast equilibrium. Equilibrium is an alteration spell that turns health into mana. This will get your alteration and restoration skills up to 100 relatively quickly. If you don not have the spell, then stock up on magic potions and cast a spell in whatever field you wish and continue to cast it until your skill increases.
Smithing: Once you have a moderate amount of coin built up you can start grinding your blacksmith skill by buying a large amount of iron ingots from the blacksmiths and creating as many iron daggers as you can and sell them right back to the blacksmith. When one blacksmith runs out of forging supplies, move on to another one and repeat. My personal route was: Battle Maiden, Skyforge, Riverwood, and Solitude smiths. By the time you get back to the starting one on your route, the smiths should be stocked back up on iron ingots.
Enchantment: As for enchanting, if you complete the "Azura's Star" quest, you will end with a refillable soul gem. If you obtain a staff that absorbs souls or have a spell that allows you to absorb souls, you can infinitely fill the star and enchant iron daggers (filled with petty) over and over again.
Archery, One Handed, and Two Handed: If you have a (relatively) weak unkillable enemy available (such as a legate in the Rift Imperial Camp if you joined the Stormcloaks), you can increase your skill over and over while you work on your armor and blocking skills at the same time.
Armor and Block: You can go against relatively weak enemies when you are strong and let them hit you over and over. It will raise your armor (and block) skill up without much effort on your part. For blocking, you should have a good amount of stamina potions as blocking uses up your stamina. If you wish, you can do this against an unkillable enemy (if you joined the Stormcloaks there is a Legate in the Rift Imperial Camp). This will allow you to work on another skill at the same time (see above).
Tutors: If you have a good amount of coin built up you may spend it on tutors to increase your skill. Each level, you can increase skills 5 times. You can increase 5 skills once or 1 skill 5 times, but you can only increase a total of 5 times per level. If you wish to do this, it is best to do this early on, in order to receive the max benefit from the tutors. You can pickpocket the money back, but only when it is below 2 or 3 thousand (assuming you have a high pickpocket), after that, it is impossible. You can wait 24 hours and that person will have 1500 gold you can pickpocket, but if you give them anymore than that it will be lost forever. Therefore, this is only effective when you start early and continually invest towards the skills every level.
I would like to thank (all of these are their Xbox GamerTags) Mstrofdashadows, StNowhere, Tyhonpholus C, Cloudbuster B, THE IRISHMAN 35, Fiire Fist Ace, MEGAMAN962, and As R0me Burns for commenting and improving this solution on the Xbox TrueAchievements.
If you have any ideas on how I can improve this solution, I'd love to hear them! There may be something that isn't here that should be, or an easier way of doing this. I'm always open to suggestions. If you notice any typos or poorly phrased sentences, please let me know.