After you receive the Mechat on Disc 3 you will notice new symbols on your world map, the yellow symbols and orange plus symbols are places where you can get new parts for your Mechat, and the blue plus symbol is where you will go to equip these new parts. There are 9 pieces in all.
Tackle the yellow symbols last as they consist of a dungeon that you must go through to get the piece.
To start we will have to go through a dungeon, The Sea Cube, this due in part that after defeating the Sea Dragon at the end you will receive the Black Device, which is needed to open many of the chests containing the missing parts.
1. Defeat the Sea Dragon, then open the chest behind it after receiving the Black Device for Laser Barrier Parts
2. Lal Mountains Camp, open a chest with the Black Device for Missile Upgrade Part B
3. Kelaso Village, you will need the Black Device for Coating Part B
4. Eastern Deserted Island, here you must defeat the Ghost Yeet that appears, after defeating him you will receive the Heatsink Parts
5. Enter the Aurora Ruins east of the massive snow fields, here you will have to fight the Stonesaurus, defeat him and Toripo will give you Lock On Upgrade Part A
6. Exile Forest Caverns, after you save Gulu Gulu it will be on the far wall, the Black Device is required for Lock On Upgrade Part B
7. Ancient Ruins Forest, which is West of the Gul Mountains. After going through this simple dungeon you will fight Land Shark C, defeat it then open the chest for Weapon Parts
WARNING: Before you head to this next spot you will enter a Mechat shooting stage, you can get an achievement here for shooting down all the machine guns (damage doesn't matter).
8. Upper Mecha Base, it will be in a chest right before the lift to the 5th floor, which contains Coating Part A
9. Mecha Base, also in a chest before the elevator to the 5th floor, contains Missile Upgrade Part A
Now after obtaining all 9 parts head over to the blue plus symbol on your map, enter here and all your new parts will be equipped.
Congrats on your new fully upgraded Mechat!