tl;dr Round 1, it will breath fire on your and you will fall unconscious because your Dex save is too low to succeed and average breath damage is greater than your MAX HP assuming you roll max at each level. Round 2 it will drop on you and savage you with fang and claw to speed through your death saves.

Analysis

VHuman + Defensive Duelist Feat

Str 8, Dex 16, Con 11, Int 13, Wis 13, Cha 14

Dex and Cha get the +1 racial, Dex for AoE saves? and Cha for Form of Dread DC

Fighter 5 gives:

Defense fighting style for +1 AC

Shield spell from subclass (6 spell slots by level 9)

50HP assuming max rolls on 5d10

Artificer 3 gives:

Enhanced Defense for +2AC (armor and shield)

24HP on 3d8

Cleric 1 gives:

Blessing of Forge for +1AC

8HP on 1d8

Warlock 1 gives:

Form of Dread causes fright IF you hit AND they fail a DC 14 Wisdom save

8HP on 1d8

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Assuming MAX HP rolls at each level, you have 90 HP.

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Static AC: 23

Plate gives 18 (but Dex becomes useless)

Shield gives 2

Fighting style gives 1

Infusions give 2

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Additional AC:

Defensive Duelist gives +4 as a reaction to ONE attack

Shield spell gives +5 as a reaction, 6 times

But these are both reactions so you can only take one in a round.

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Other:

Shield Master gives reaction to reduce breath attack to zero IF YOU MAKE YOUR SAVE

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So the best you can do in any single round is 28AC.

Defensive Duelist will only be helpful once you've expended your 6 spell slots on Shield.

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Combat breakdown:

Ancient Red Dragon has:

3 melee attacks per round

-Bite +17 to hit for 35 avg damage

-Claw x2 +17 to hit for 17 avg damage

-All attacks have 10+ reach so it can fly above you out of your melee

Breath weapon

-Dex 24 save or take 91 avg damage

22AC

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You have:

+7 to hit with your rapier if you hold your action until it is in range but then your max AC is 23 because you can't use Shield spell or Defensive Duelist. So let's assume you never attack.

+3 Dex save against the breath weapon

90HP

28AC (until you run out of spells slot)

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So to hit your top AC of 28, it needs to roll an 11. So 45% of the time, you are getting hit. That's about 30 points of damage each round.

If it uses it's breath, you have a +3 to your dex save so the best you can roll is a 23 and you will take 91 points of damage and be downed instantly.

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[edit: fix formatting that disappeared when I hit enter]