Most difficult Fire Emblem boss, in your opinion. *Spoilers*

[Dark Sonic]

[Neofox]

[Lord Fuckboy]

Still the same boss..

[Ice Dragon]

[camus the dark knight]

36 STR + 22 from Double Bow + 5 from Ena's Red Wave = 63 - 50 = 13 x2 = 26

He will deal 26 damage (Even more on easy because of the +5 STR If I must) per fight, then you have your Heron for 52 damage... Then we can add

He's down to 48 HP now...

Tibarn: 36 STR (Base, could be higher)+ 20 from his beak + 5 from Ena's Red Wave = 61 - 50 = 11 x2 = 22

So here is 22 damage, that leaves him with 26 HP...

Caineghis: 44 STR (Base, could be higher)+ 22 from his fang + 5 from Ena's Red Wave = 66 - 50 = 16 x2 = 32

Another 32 damage, He's dead assuming they all hit, in case they didn't...

Ilayna: 32 MGC (Level 20/20/10 average, she very well could be a higher level)+ 36 from Rex Bolt (12x3 for effectiveness) = 68 - 46 = 22

An additional 22 damage. And she will be attacking last, so she will kill him likely and not have to fear his counter. I am sure there are also others that can harm him for additional damage (Ike can give 20 or so per round with Red Wave I think).

This also isn't factoring in supports...

[Dark Sonic]

[Lord Fuckboy]

As for Elaice, I don't know about you, but I never had any problem training her in Part 3. All I did was make sure she was the one killing as many of the Dragonknights as possible and finishing off anything that didn't get killed in one round by Wayu or Nephenee. (My usual strategy is lure-swarm when I'm in a huge map, so training lower-leveled characters isn't much of a problem.)

I've had a hard time because Ike's units are borked and have a hard time leaving enemies alive enough for Ilyana to finish them off.

[yoshmaster5]

Well, I'll analyze by the games I've played, and decide from there.

FE4: Yurius is a demon... when attacking with anyone BUT Yuria with Narga. The fact that a lv. 19 Yuria with Narga can do tons of damage, and a high level promoted Yuria utterly rapes the Loputsu incarnate. This makes him fairly low, personally. I've found Alvis to be much harder than Yurius, and yes, not having the broken-ness that is Narga is one reason.
Alvis has maxed stats, Fala Flame, and tons of avoid. Celice with Tyrfing with most maxed stats will take a long time to bring him down. He would even have better stats than Aless, because the Tyrfing now makes Aless's +10 MDEF from the Mistoltin look weak, considering the other bonuses the Tyrfing gives, and because Alvis has Awareness, making Critical useless.  Shanan and whoever is using Holsety; be it Corpul, Arthur, or Sety; are able to double attack; but are unable to do significant damage without insane luck. Faval does have an advantage because of the Ichival's strength boost, as does Althenna, but Alvis still does ungodly amounts of damage. Overall, I found Alvis much harder than Yurius.
Ishtar is worth a mention, but because she doesn't have Awareness, a number of things can happen: Arthur/Sety Criticals with Holsety (Plus the Triangle advantage and insane speed boost), Shanan pulls off Meteor sword, Aless crits with the Mistoltin. That's only the holy weapon users too... Lackhe could pull of Meteor sword with the Hero's Sword, or if Holyn is the father, Moonlight sword. Both are almost instant death, and the same applies for Shakasher. Too many things could go wrong for the poor sage to be a major concern, IMO.

FE5: ... Ledirick died in one hit to Leaf. ... Berdo is a pain to get to, but when he's reached... that thing would die to Marty. next.

FE6: Zephidel is tricky. He has decent stats, and the Exxacus is an awesome weapon.  But, he can be taken down easily. Fazilla, Forblaze, Roy, Mulgre, or the Malte can defeat Zephy. Granted it will be a pain, but it will happen.
Idoun is one rounded by Roy and Fa.  Aside from that she is difficult, but that is akin to the utter Yuria rapeage.

FE7: Nergal... -__-;
Aureola or Armads destroys this prick. When Renault can OHKO you... as a boss, that's sad.
Fire dragon? Armads + Forblaze/Aureola kills.
I don't mention Luna because that spell destroys everything. See SDA's FE7 speedrun, Athos Luna-crits both Nergal and the Fire Dragon. One rounds, both of them. Next.

FE8: Not any debate. Fodeath dies so quickly, it's not even funny. Myrrh critical, Anyone with a S-rank weapon really, he puts up more of a fight than Idoun, but it's still just sad.

FE9: Now, a challenge. The Black Knight is so luck reliant it's scary.  Luna owns Ike, and you need to pray for Aether to activate. Multiple times. Maybe Nihil/Wrath works, but I haven't tried it.
Ashnard is also tough. Seeing as he can 2-round almost everyone makes Fortify a godsend, and because only Ike, the Dragons, and the Laguz Kings/Giffca can hurt him makes Ashnard a tough nut to crack.  It is less luck relaint, but Ashnard will still be deadly.
Plus, he revives on HM. And moves. Meaning, you'd better hope your healers/other units are protected, and that Ike has good enough stats. This can be very difficult.

FE10: VERY, VERY tough final bosses. Exculding Sephrain, of course.  Ashera is very difficult... using the +10 magic defense tiles seems to be the best plan of action for anyone she targets. (STOP ONE-SHOTTING MY HERON!!!) Besides, the auras are very annoying to take down. Fortify is again god.  Ike has to deal the last blow, but then again... you'd be using him anyway.
As for the ...
Very tough. VERY, VERY, tough. The fact that he doesn't go after Kurthnaga or Ena is moot really, because they won't do much damage to him anyway unless you heron abuse. A marksman and anyone with Awareness seems to be the best option here. Marksman attacks from range, while awareness people attack without worrying about the mastery skill. Plus, if you decided to bless a long-range Magic tome, you can rain thunderstorm, meteor, Blizzard, Fenrir, or Purge on the fool. Then again, you can do that with anyone. either way, he's still a very difficult boss, and one of the few FE bosses that needs some planning or strategy to take down without loosing someone.

Overall, I'd say the hardest boss (aside from the Luck-reliant BK duel in FE9) is either Alvis, Ashera, or . I've explained why I think so, and since they are the few bosses that can put up a good fight, it makes the games more interesting.

[Ayanami]

FE1-Camus-He is the hardest as he has a great chance at killing your units due to high speed, without capped speed he will likely double you with the Gladius.

FE2-Judah-Well he is a pain in the arse as he cannot be attacked, but doing that enough times will get it to eventually work, as for getting the Dragonshield item, good luck.

FE3-

Book 1-Camus (See FE1's information.)

Book 2-Medeius-Yep, this time you will be attacked by a swarm of Dar Dragons that will always be dealing 22 DMG no matter what as the dmg cannot be neglected and that even with capped Speed and Luck, you will still have 30% chance at getting hit by the Dark Dragons' Dark Breath!

FE4-Ishtar-She can MOVE, dish out around 62-64 Dmg a hit with Thor Hammer, and that without Celice or Ares, any other unit will likely get doubled and killed.

FE5-Cyas-His RNG raising ability says it all, 40-50% more Avoid and Skill to all enemy units on the map, with him around you will lose troops.

FE6-Murdock-He will be troublesome to kill that is if you are trying to access the gaiden chapter, and without Lilina's help this task cannot possibly be done.

FE7-Linus and Lloyd (Final Chapter)-Wtihout berserking or using a Sleep Staff, they will be tough to kill together.

FE8-No Comment.

FE9-Black Knight-Definitely, as this fight is only won by luck of thr RNG of Aether.

FE10-Ashura-What others have already said, she is the toughest FE boss that I have ever faced and it is most likely that you will suffer casualities. Nasir is the only unit that I know of that can possibly survive her wrath.
       

[yoshmaster5]

I would have mentioned Murdock in FE6, but teh fact that the Armorkiller utterly destroys him... kinda drops the difficulty. 

It's sad too, because he is an awesome character.

[Mhoram]

FE3: Camus
FE4: Those three Peg sisters in the last chapter. Honestly, with Ishtar I can limit her movement through the canyon with celice and aless (I usually give aless a res +5 ring). But the peg sisters, I have to take them out in one hit before they can rape one of my weaker characters with those earth swords.
FE5: Maybe Reinhardt? Played on elite so I'm wuss.
FE6: Those berserkers in the desert chapter. Chasing you and all, it made it tough for me to deal with them.
FE7: Mebbe ursula. Sometimes I forget about her being in the Fog of War and she will screw me over with bolting, landing a quick kill.
FE8: That sleep spell by formortis took me by surprise once, I only won with a critical I think. Not that he's hard, but he was harder than the rest.
FE9: Hard Ashnard or Black Knight. BK...with the average 20/20 Ike w/ aether, and a promoted mist you have a very good chance to beat him. As long as you are able to figure out when you should restrain yourself from attacking (if mist has already healed and then you have Ike attack, you run the risk of getting x2 luna'd) you can usually win.

Hard Ashnard beat me the first time I fought him (well, he didn't beat me, but he killed Kieran which was enough for me to reset), but once you KNOW he's going to move on you you can use Ike to clean off the right side of the map, and then move to the top to hold the dragons, paladins, armors, bryce, and ashnard. One sage with enough magic (soren, mist, rhys should all achieve this, I don't know about Ilyana) loaded with psychics, fortify, and ashera staff can keep Ike alive long enough (you can use reyson and your dragon as equipment mules). Two, or one sage along with reyson, will let him attack every turn. Send a flier around the back to take out the mage on the balcony with psychic who can heal ashnard.

With Ike the only unit near him, Ashnard will stay one move away. I usually don't even send in nasir; while it might be possible to have him run in, hit, run out for a bit of extra damage, I'm always worried ashy will switch to following him.