You need to level up your BP level towards the Dragon Slayer class. You'll get Lloyd by doing so.

Many of them are related to the achievement, so you'll need to do it anyway. However, some of them are not, and you can skip some of them if you want, like winning 500.

Do note that these BP achievement-related Steam achievements pop up the moment you unlock them in-game in the main menu, rather than the moment you fulfill the condition. So if you were doing non-stop story mode and unlocked an achievement while doing that, it will unlock after you see the ending credits and return to the main menu.

1. Clear each of the 5 characters' story mode.

2. Clear story mod in Alternative difficulty. You only have to do it once, not for each character. You don't have to clear Story mode in Advanced difficulty, while you can for like grinding exp, BP, monapoint, it doesn't give anything unique, nor related to an achievement.

3. Beat Arcade Mode with everybody, including Lloyd

4. Level up all your characters to 99
(1) It gives you an item. (Which is related to an achievement)
(2) You gain BP by leveling up the characters to 99.

5. Clean Up

These are cumulative, and you don't have to do it in a single time.


The Power of Friendship: Used support actions 100 times.
Mona²⁰⁰:Visited Mona's Shop 200 times.
Burstin' Makes Me Feel Good: Used E-Burst 100 times. (IIRC, there are no tutorial popups for this one. Check your key settings, and check the in-game tutorial for what it does.)
Oh, and a tip, after defeating the final boss, you'll get a brief moment until you see the victory screen, since there is an animation for the dragon collapsing. During this time, using E-Burst doesn't cost HP. So mash E-Burst while you can.


"Destroyed 500 objects" is also cumulative, while not being a Steam achievement, but only a BP achievement.

You can unlock the achievement while playing in a multiplayer mode. But if I get it right, the 1st player must be the one who fulfills the condition. (There is a chance that I mistook it, though.)

So you can manipulate the situation by playing multiple characters all by yourself.
=====================================================

Sick Day: Afflicted with every status ailment.

This is not cumulative and must be done in a single battle, and your character has to be affected by every status alignment at the same time. 10 icons, but do note that things like minus sp- also show up, and they don't count. The status alignment that is shown in the tutorial is the only one that is counted.
There are accessories for this, but only for 7 kinds. So you have to earn 3 by other means.

According to CMDR Sho, Gilbert will sometimes give all status alignment, and you can use this to earn those.

Below is some method I used.

I beat them by: 1. Any 1st character 2. Tita with a bunch of accessories and Campanella (random status alignment on a hit) as support. 3. Cruxie with accessories and Campanella 4. Kloe CPU.

1. 2nd, 3rd, and CPU team up against the 1st player
2. 2 and 3 activate support
3. Cruxie does provoke
4. Tita does the machine gun
5. Mash attack buttons.
======================================================
Made of Sapphirl: Win a match after surviving more than 13000 damage

This is somewhat misleading. What this means is:
(Your character's initial HP) - (You winning character's ending HP) > 13,000
I beat it by giving Dogi an HP accessory.

==================================================
Building My Museum: Completed the Material Collection.

While you can earn some of them via spoils of battle, you can also buy them in the Mona shop.

Do note that some of the OSTs are not unlocked in the shop until you have unlocked the relevant stage.
========================================================
Steam only achievements.

They're not listed in the in-game achievement and will be unlocked as soon as you meet the condition. I've listed them here since it is hidden, and to save you the time of clicking the achievement to see the condition.

Reluctant Leaders: Win a match as Kloe with Olha as a support.
Bring the Hammer Down: Win a match as Cruxie with Mustafa as a support.
JoJo's Unusual Predicament: Win a match as Joshua with Josette as a support.
Oh, There She Is: Win a match as Aisha with Sigroon as a support.
That's Fact Up: Win a match as Adol with Dark Fact as a support.
A Match Made in Heaven: Win a match as Olivier with Scherazard as a support.
Ya Gotta Have Green Hair: Win a match as Elk with Kevin as support.
Ancient Ys Vanished: Win a match as Adol with Feena & Reah as supports.
Special Support Section: Win a match as Lloyd with Elie as a support.
Carried on the Winds: Win a match as Mishera with Tia & Maya as supports.
Big Shoes to Fill: Win a match as Tita with Yunica & Hugo as supports.
Big Boy Beatdown: Win a match as Dogi with Zin as a support.
The Best and Worst of Ouroboros: Win a match as Renne with Gilbert as a support.
Stoddart Stalwart: Win a match as Chester with Elena as a support.
0 and II: Win a match as Loewe with Campanella as a support.
This Shouldn't Traumatize Anyone: Win a match as Geis with Ernst as a support.


=======================
etc

If I got it correctly, BP achievement "Beat Arcade Mode unscathed" is for clearing any of the arcade mode stages (not the whole walkthrough) without getting hit according to CMDR Sho
"Dealt over 5,000 damage at once" BP achievement means 5,000 during combo, not a single hit.