Fight 1: (2 Parts) Not terribly difficult. I actually learned to do this fight at least partially outside the skells just to save some energy for later on. My Cross runs a pretty potent Thermal build from Samurai Gunner so damage on the target wasn't too huge a problem. It will periodically send out support orbs at specific HP phases (start and ~50%) that can wreck you if not taken care of quick enough. Around 30% it has an invincibility shield granted to it (and some mild HP regen) from the orb in the center of the arena. You only have to kill the center orb during this phase to stop the shield, but the orbs surrounding it take only 1 damage and are taken out quickly with gunfire. The skells help to clear the orbs during those phases but overall are not entirely necessary with good skill/art leveling.
Fight 2: This is what really got my blood boiling. You face an average opponent, but theres 10 of them. Yes. Ten. Right after a pretty long boss fight. This is why I wanted to save my skells, simply take flight and command everyone into the skells and snipe them all from the air. If you really want to take them out on the ground without skells, AoE skills are your best bet. Be warned though, I set up my Lin to be pretty tanky as far as tanks go and she still gets ripped to shreds with 10 things beating on her.
Fight 3: If you're quick enough, you can get off one G-Buster or Scythe hit before your skells are drained of all fuel. So this fight will be done entirely without mechs. It isn't entirely difficult from what I recall, but I was also still fuming from the fight right before. Nothing stood out about it, aside from who it was you were fighting. Target and break limbs if you want, but you can just zerg it down.