A tonberry first appears in the final story chapter "The Cave at Nostal: Final Chamber" (3rd Cave chapter). The tonberry appears on the very first screen of the chapter, so there is no worry about saving up your armiger power until it makes an appearance. Since it appears on the first screen, simply pause and restart from checkpoint if anything goes wrong.
You are most likely aware by now of what maintaining a combo towards the armiger consists of, but if not, it is simply avoiding damage while attacking. Does not need to be consecutive, or even the same enemy, just take your time and pop shot if you're not confident.
Most of the enemies on this screen require semi-careful attacking to ensure your combo is unbroken. The red skeleton (shield bash, few quick strong attacks, repeat), green cactuar (can reflect needles until dead, not needed for gaining combo), and gold cactuar (hit once, move, hit again, move, repeat).
A few words of wisdom: Avoid the tonberry's lamp glow because it slows you down (or use a blizzard magic attack to extinguish it), and save the armiger until the tonberry is the last enemy on-screen to make sure the armiger attacks it. If you're thinking of attacking the tonberry to gain combo, be careful. In classic FF fashion, all it takes is 1 knife hit to kill you. Fear the grudge!
Alternate Method if building the armiger is giving you a hard time: There will continue to be several tonberries in the second and third screens as well. Following the tonberry/iron giant battle there will be a boatload of flans; it is very easy to build up the armiger here, as a tonberry appears immediately following the flan. Could be harder to control who the armiger hits however.