Majidonga is similar to Dodonga, but stronger, more durable, and with an extra attack. See the "Majidonga" page for further details.
The fog makes Majidonga harder to see, but even if it's further away, you can still make out a faint outline. Your Patapons can attack as normal, and if Majidonga is far away, it probably won't hit you with its attacks, so the fog is the only real hindrance if you want to begin attacking the boss (i.e. while it's sleeping) from a certain distance. If you really need to see the beast, Tailwind or Rain Miracles will dispel the fog for a while, with the latter also decreasing the effectiveness of the boss' fire attacks.Basic tactics work well here, but Majidonga is a lot tougher than a comparably-levelled Dodonga, so don't expect a short fight. Also, its new Roar attack will devastate your Patapons even if you defend from it, so extra improvement of your army may be necessary. Make sure you avoid Rarepons weak to fire and Ignite effects: in addition to its fire breath, Majidonga can set them alight with its Roar, which has enough range to hit every unit. Knockback immunity may also prove useful, as Majidonga's Headbutt and Roar will send their victims flying.
If you just can't tank the damage, consider dodging back with the PonPata song, which will neutralize everything Majidonga can throw at you, apart from the Roar. The PonChaka song is handy as well to minimize the Roar's damage, but the setup time makes it a bit luck-based. It's more than possible to beat Majidonga with either song of course, but be prepared for a tough fight.