Party: Mage (elementalist), Melanie, 016, Gobby
The cannon is not susceptible to any type of magic, but Commander Llona is very susceptible to elemental magic (especially ice and bolt)
You need to concentrate on taking out the commander while damaging the cannon enough for the engineer to have to fix and it resets to 20% charged.
Mage-no effect against cannon, so keep attacking commander with elemental magic
Melanie-use predominantly against cannon. I found her triple attack worked well, but her break blade worked even better because it allowed 016 to get a free shot in
016-can be used effectively against both cannon and commander. Just her routine attack x2 against the cannon and setup strike and cripple against the commander. You can try her sealing sweep, but I was only successful with that once.
Gobby-Use his dance and shout and keep renewing those states. Gobby can sometimes get a good physical attack against either the cannon or the commander, but I found him best used as an adjunct, supplying HP and AP potions, and even healing herbs, when he wasn't dancing and shouting.
When Commander Llona heals herself, you'll know she's almost done for. Go for the kill, unless the cannon has reached greater than 40%. Always make malfunctioning the cannon your top priority. The commander isn't as much of a threat.
Once the commander has been defeated, go for the cannon. This will probably take several rounds. Mage is totally ineffective against the cannon and he can't heal with spells, so he'll be helping Gobby with potions and herbs. Remember to keep Gobby dancing and shouting when these states wear off. If he can get a shot in every few rounds, then that's all the better. Melanie is the real cannon buster with her triple strike and her break blade and 016 will sometimes get a few heavy duty strikes in as well.
I'm sure there are other strategies, some maybe even more effective this, but this worked for me.