If you fire a charged light beam shot at him while in either form, it takes him out all of the way. Basically, if you hit him during the tunneling phase, it knocks off his armor entirely, instead of having to pump missiles and charged power beams into him. Then, when he's attatched to the ball, if you hit him again the armor on his head is destroyed, immediately letting you get inside him. (The whole sucking you in sequence) Use a normal bomb to blow him up while inside.
If I counted right, you can eliminate Amorbis completely with about 60 light beam ammo, if you hit every single time with the charged shot. You may need to hit him more if your shots aren't entirely accurate.
If you are having trouble, stay in the light crystal areas and watch the dirt trails.
Bombs placed outside of Amorbis during his stunned 2nd form works just as well as laying them in his stomach. It seems that any bombs placed on a line will damage Amorbis, not just near his mouth. Further testing is necessary to confirm what exactly damages his mouth.
If you want to scan Amorbis, you can do it without loosing any time. Just shoot him the first time wth a charged light beam to knock of his armor, then scan him. While you're scanning him he will go down again, dont stop pressing L, hold it, your visor will turn down and scan something under the ground. It's Dark Amorbis! You have enough time to scan him completely and charge the light beam until he's finished with his "transformation". In the next round you just have to scan the normal amorbis again for 1 second or something.