PAINFUL AS SHIT. This achievement requires you finish all the free missions with one character. You can do this on easy difficulty, which would make you think this achievement is easy. That would be false.
Every stage is easy except for the two survival missions. For these, you'll need 190 kills in the first, and 500 kills in the second.
The first one is a bunch of standard HP enemies of varying type. Each wave gets progressively harder. Every once in awhile you'll get a wave that has a swarm of smaller enemies. You'll be wanting to kill all of these, as they have a chance to drop a life potion. On top of that, they disappear after a time, and every kill you miss means longer you have to survive. They are also massively easier than most waves, so take advantage.
There are two alcoves with chests, and the chests in the front have life potions, the ones in the back have battery rods and bombs and the like.
The main problem is most of the later waves have elite enemies in groups. The problem with that is in the campaign and other free missions, elite units are capped at one because they are cheap as fuck. Not here. You'll be faced with as many as four of them, and sometimes they will be grouped with smaller enemies. Have fun with the wave that has three of the dragons.
After you have over 190 kills, you can keep going (why?) or die and win the stage.
The second one requires 500 kills, but unlike the first survival stage, it ends once you finish the last wave (you'll have around 500 kills). In this stage, the enemies start out being one hit kills and gain more and more HP as waves go by. Like the first, they get progressively harder.
You'll eventually be fighting waves with these stupid fucks (why yes, I am raging a bit : p) that can cast a curse on you that disables ALL YOUR ATTACKS. You could dispel it, but you'll have it cast on you so many times you'll run out of dispels way before you finish the stage. Your other option is to kill them, but since they can curse you, and a bunch of other strong types spawn along with them, it's nigh impossible to kill them before the horde comes down on you.
To date, I've only finished it with Ky and Sol. Sol is very easy, his gunblade (neutral stance + Y. Neutral means you aren't moving the left stick) is BADASS. Hits 5 enemies for good damage, knocks most types into the air, and is ranged. I've found the key to these stages is using ranged attacks and keeping your distance. Let your tension build up and spam gunblade at everything. Use your dash to get away and let your tension build up.
You'll be needing to strafe back and forth a lot, as the archers, the knights, and a few other types have ranged attacks that can hit you for a decent amount of damage. However they don't generally lead their aim, so you can strafe to avoid.
This method is very tedious and annoying, but once you learn attack patterns and movement you can minimize damage and make this somewhat easy, just annoying and time consuming. I think it took me 30-45 minutes with Sol, and closer to an hour with Ky.
You can also use Ky, as his neutral+Y attack is also a ranged attack, but it does less damage than Sol's, stuns them for a second instead of knockdown, and only hits one enemy. I haven't played around with the other characters much yet but Sol is the best choice for this so far.
Note there is an achievement for finishing the free missions with each character, so you'll have to do it with everyone eventually, I'm just saying Sol has been the easier so far.