Actually, Alyut has a lot of advantages over mega without even trying to rationalize attack animations. Just in the raw numbers, Alyut is going to beat him out.
Mega HP ATK DEF REC
Lord 5,215 1,982 1,264 1,910
Alyut
Lord 6,182 1,755 1,920 1,811
Those are the 6* forms. Alyut has more HP and DEF meaning he is going to survive getting attacked better and keep dealing damage, while Mega could get tapped out easier due to the low HP and DEF he has. Mega also has too much rec and not enough hp, so a lot of healing is going to waste on him. Alyut is more balanced in this regard.
Aside from that, if you weren't already aware, the tuesday, wednesday, and thursday dungeons are the best opportunities for evolution materials. This allows you to avoid trying to do it forcibly through the quest missions. A fully leveled up and evolved team will waltz through Cordelica without breaking a sweat. The initial hurdle will really be getting your totems, but after you get the first one done, the rest come much easier. The only downside is that the cost goes up with the evolutions Alyut 12->16>26/Mega 5->8->12->22, so plan accordingly prior to evolution (cost maximum increases with
summoner levels).
Should you also get Alyut up to his 6* form, you may not even need to bring merith anymore since he has a heal over time attached to his SBB, in addition to BB charge rate. Getting some of the more fragile units out of your rotation will reduce the amount of healing items you use turn to turn and should swing those fights for you much quicker.
Other stuff in general. That particular fight the enemies cause injury, so bring tonics. Guard with softer units like merith every round they aren't using their BB. Divine lights can be more useful than regular cures in a fight with a lot of AOE. Ares/holy flutes can be very useful at building/generating BC for BB use. If at all possible, lead the fight off with BB spam in the first round to try and eliminate the other 2 units. If mifune and mega die, it could also be more beneficial (item wise) to leave them dead if AOE spam is what is knocking you out and let the tougher units like kikuri wear undine out.
Ares elixers could also be a good one to bring, since you don't have the luxury of a mono-element team and take advantage of ore/stones. Although, you will need access to gold drops to make them which is possible by upgrading the river to high enough levels.
That one is still more of a warmup for that series of maps, but with a couple of tries I'm sure you can get through it. The light and dark maps get harder a lot quicker IIRC in that map series.
