Providing a guide on one of these level 30 achievements to help some of you. These really aren't a grind even if you want to take it slow, but here's a few tips for leveling classes to 30 as quickly as possible. This guide will sort of abuse the Bounty system in this game.
First, you should focus on one main class. Find what you like (Ranged characters worked best for me), then get them up to level 30. As you level up and complete more expeditions, you'll be able to run the Hard and Very Hard versions of those Expeditions. These provide more XP, helping things go quicker.
Next, accept a Expedition at the Quest Counter. Then, make sure you first search on the "Current Block." This will leave you in the main area before you enter the ship. Now, scroll over to your Bounty page. At the bottom, there should be something that says "Available Bounties for Current Mission." Click that, then select the applicable bounties. If you want to "Search Multiple Blocks", go up to the Quest Counter and select the same quest again.
Now, run through the mission with your main with another sub-30 class as your sub-class. Take your time and clear it fully. Quite a few bounties require you to search most of the map so you can find the more rare enemies who spawn. Some also require you complete it in a certain time, so be mindful of what your strategy will be.
Now when you get back in the ship, go to the Class Counter and change your class to a sub-30 one. Now, search the ship and complete all the bounties from the previous mission.
Switch back to your main and select another expedition and repeat the process. With this method I had everyone to 30 in a few days. It gets a little annoying going back and forth from the Quest Counter, but it saved me from playing some of the classes I disliked.
Another thing I would do is, following the mission, if I made no progress on the bounty I would just abandon it. That way you have more room for the next one you do.
The achievement doesn't unlock when you hit level 30, switch your character's class, then go back to one you've gotten to 30. It will pop afterwards.
This is a great game, so it may be worth using this method only on Classes you hate to play. Have fun with this one, and feel free to let me know who this can be improved.