Both of these achievements can and need to be acquired really early on in the game.
They are NOT mutually exclusive, as their names might suggest. You can get both on the same save.

Bad boy
Threw Geddy into the clouds! How rude!


Once Geddy has joined your party, toss him down the ledge and it will trigger a cutscene. That's basically it.


Good boy
Tried to report to Asio at the first sign of trouble.


After you earned the achievement above, grab Geddy and fly back towards your house. On the way there a cutscene will ensure, where you'll once again meet the 2 owls, which Geddy just saved you from. After that cutscene, fly upwards, past the cannon, past the hot spring and take the way to the right to get to the scientist's house. Enter it to unlock this achievement.

Hot Spring Mastery
Learned how to cope with the heat in Toby's hot spring.


The hot spring is located in the starting village, just above the giant cannon, where Geddy can be seen for the first time. Just enter the hot spring and wait a few seconds - Toby will start a conversation with you on his own. He'll tell you how to cope with the heat and you get the achievement simple. (Even if he disapears after the Advent attack you can still get the achievement just head on over to the spa and wait for a few moment and Geddy will say the same line as usual)


Music Master
Played Otus's song on Bomboman's drums.


A little way left of the hot spring, talk to the Bomboman several times and he'll play you a song. Pay attention to each bongo he hits - or in this case I'll give you the rhythm:
(Right,Left,Right,Right,Right,Left,Right)
Enter his house and play the bongos upstairs. Once you put in the "code" you'll earn the achievement and a key which will:
Open a hidden wall in Mesos before finding Twig's house for the first time.


Oops...
Beat Geddy 1000 times.


It's not really hard and not a long process. You can just put Geddy in a corner and hit away.
(Phones or Tablets might be required to lessen the boredom you might develop while doing this)


Flight of the Boguin
Cleared the Boguins' Cannon challenge.


When you rescue all of the Three Boguin bros you unlock a cannon mini game, just finish the course and you get the achievement but if you're going for the Treasure Seeker Achievement you have to collect every ring in the course. Luckily they updated the game on December 6 so that you can collect the remaining rings after you failed.


Reminiscing
Listened to the shell near the old ruins.


(Please read the previous achievement to do this ^^^^) Once you aquire the shell, head on over to Tropos and walk all the way to the left where the tower is and you'll come upon a patch of dirt with some rubbles.




Ancient Memories
Collected the Golden disks.


Collect all 3 golden disk inserted or not

Screenshots provided for 2 are from Jenoms
Screenshots provided for 1 and 3 are from Akka

1st:


2nd:


You'll need alphonse for this one and head to Strato an tell you reach this part shown in this image. Go to the left where Otus is facing. Follow the path and go up once you reach to those spikey balls rotating in a circle and you should come up to a tree shown in this image



3rd:



Trinket Master
Mastering trinket collection at Buccanary's!


Trinket Grand Master
Unlocked every trinket from Buccanary's shop.


Well... Collect all of the Trinkets from Buccanary wares.


Treasure Seeker
Collected Buccanary coins.


Treasure Seeker Grand Master
Collected all Buccanary coins.


Collect ALL Buccanary coins you need to collect 2860 coins. Collecting a chest after getting 2800 will get you 60 coins in total (Normally amount 30) head to the shop once you get 2830 and it'll instantly give you 2860.


If you enjoyed this guide please leave a like and share this. It's my first guide ever made so please don't torch me. Thank you for reading!!!