During this tempest trials, I’ve faced many different heroes, some of which are more annoying than others.
Again, here is my team that I used for the majority of the Tempest Trials:
My top 5 most annoying units may differ from your top 5 list. Feel free to discuss in the comments about your top 5 most annoying units to face.
My list contains mostly people that I cannot ORKO (one round KO).
Notable Mentions:
Palla, due to Wings of Mercy. However, her attack is very low and does not kill anyone on my team.
Faye for Wings of Mercy, but her speed is so slow that she does not double my Reinhardt when I have horse emblem buffs.
Hector, since I do not have Sacae’s blessing equipped. However, I could easily equip it and defeat Hector easily.
Eldigan and Roderick, due to Lunge, but they are very easy to defeat and are both ORKO-able.
Unit 5: Camilla
My Reinhardt cannot ORKO Camilla. However, my Brave Lyn can do it.
Unit 4: Sheena
This may come as a surprise, but no one on my team can ORKO Sheena. 
My +Atk Reinhardt cannot do it and neither can my overpowered Brave Lyn. Sheena requires two attacks to defeat, which is very, very annoying.
Unit 3: Arthur
Neither my Brave Lyn or Reinhardt can ORKO him, which means that I need a dancer to do this.
Arthur is super annoying.
Unit 2: Sigurd
Even more annoying than Arthur is Sigurd.
Sigurd has 3 annoying skills. All of them are basically counters to my Lyn and Reinhardt team. He requires 2 attacking moves to defeat.
Unit 1: Brave Ike
By far, the most annoying unit to face is Brave Ike. 
His skills are super, super annoying. First, he ignores my horse emblem buffs. Then, whenever he gets attacked, his cooldown is -2 each attack. Since he is doubled by both Lyn and Reinhardt, that means that he will have a charged Aether at the start of his turn. Also, since Lyn and Reinhardt are ranged units, his weapon, Urvan reduces the second attack by 80%, which is just ridiculous.
Also, he has 70 HP, and he heals himself each turn, since his special Aether is primed each turn. He takes 5-7 rounds to kill, depending on whether my specials are timed properly.
By far the most annoying boss to kill.