I'm popping this solution up for anyone looking at doing this in the last two months before shutdown - or already on their way there. This is mostly based on solo running - your mileage may vary based on how focused you are or how often you play in groups. Running groups is far faster - particularly if you grind Tubby Zombie as described below.
I have now unlocked this, and thought I'd offer a solution tailored to how the game plays right now with the permanent XP boosts:
1. Happy Jewels are easy to obtain through Orders and through daily logins. Don't be afraid to invest these into Happy Cards early on for some better gear in your favoured class. I chose to stick with Warrior, but Mage is also a viable option. Cleric isn't worth it. Look for weight 7-10 weapons with silver stars in particular as these will help you breeze through early levels where dropped items are a lot weaker - I got a weight 10 silver starred javelin in one of my early packs and I'm still using it at level 41. I bought about five packs and I have 1400 Happy Jewels at time of writing, so you definitely won't go short of them.
2. Keep your starting equipment (if you still have it). These are some of the easiest items to Awaken for:
3. For efficiency, if you have equipment from the above packs that is above weight 8 and silver starred, keep it for the rest of your grind and level them to the max. You might find better pieces around, but changing items up will give you marginal gains in time when you come to the core grind after level 30. By all means do if you want to break up the monotony, but it's not going to get you that much faster at Infection or the Tubby Zombie.
4. Level 1-30 took me 25-30 hours. I didn't play particularly efficiently either, switching between story, Infinite Dungeon and repeating levels for other achievements. I'd recommend sticking to the story, playing up to two levels higher than you currently are. Ramp up the difficulty when you can for maximum speed. You'll eventually be playing Death by level 30. I believe you can get dragged through higher-level dungeons to speed this up, but I didn't personally try that.
5. By level 30, you should be able to tackle Infection on Death difficulty, or take a decent stab at Tubby Zombie with the right tools and strong companions. I detail both grinds below:
You want to clear the second room of all enemies as well as the third room. Then in the maze, you want to take the portals that lead you South and East on the map until you find the purple boss door, killing enemies as you go - Biopurses in here are worth much more XP. Biopurses are the gold goblins that run around not attacking you - they're marked out by a red arrow above them. A single, optimal run should net you about 800,000 XP solo and take about 6-7 minutes from start to restart (or around 750k if you skip clearing room 3 and the maze enemies, which should save you 30s/1min). So in an hour, you could get 6-8M XP, depending on how quickly you jump back in. I generally hit about 5-6M/hour with breaks to level equipment/sell stuff/get coffee etc. Level 30-50 is just under 300M XP, so should take 50 hours and about. Level 30 to 40 took me just under 10 hours. So from Level 1 to 50 should take around 80 hours, there or thereabouts this way.
b) Tubby Zombie:
If you can get a session together, play the Arena Quest mission Arena of Ice. Before the session, you'll want Thunder Javelins, Brute Busters, Undead Killer and/or Spears. You'll burn through about four-six of these tools every round and I ended up completing 500 rounds - so look out for the sales on the Happy Jewel shop to stock up. If you're boosting, make sure you add everyone as friends on Live before starting up the game for the session. When you start the level, take the right-hand portal. When you load in, you should be aiming at Tubby so just let rip with the javelins/spears. Most runs I did took about 1.5mins from start to finish, with 417k XP for a four-person, all-friends run. If you can't get four people, make sure whatever spare slots you have are occupied by a spare controller as this will maximize your possible XP. In four-person sessions I averaged between 14-16M per hour - so this is 2/3x faster than running Infection solo.
Obviously, if you chance across some Goblin Bane/Undead Killer buffs on weapons as you level, equipping these to your weapons will help shave a few seconds off here and there. It all counts - by the end of my grind I had completed Infection 90 times on Death, and done 650 Tubby Zombie runs.
6. I'd complete this leveling achievement before the other misc ones like zombie kills, Finishing Move, revives, Insane runs etc. as these will slow your progress down - and they'll ultimately be faster to blitz through when you're max level. That said, doing progress to other achievements can break up the monotony in what's ultimately a long grind.
If you're just starting, good luck - happy to field questions as I'm actively playing over the final few weeks!