Barb4/Fighter 16.
Be a Champion, Crit on 18+. Better than brutal crit if you ask me. 3 attacks/round, every 2 rounds you are likely to get a crit, more if you're being reckless. Got 7 feats total, make one of them Mobility, level 3 Barbarian trait, which for Eagle means you can bonus action Dash while raging. Speed is awesome. 2 fighting styles is great, just a bit of a dip for the bonus action dash and raging. Or go Barb5/Fighter15, you'll lose a feet but have 50ft base move with Mobile which is also pretty slick. If you want to be dex based all you really lose is the damage bonus to rage but still get the far more important damage resistance, then stat wise all you really need to focus on CON and DEX and should have hardly any problem getting both to 20 in short order. Base 22 AC with just a shield, +5 to hit and damage, ton of HP, resistance to melee damage, and probably a feat or two left over for Toughness as well. Sweet and salty.
EDIT TO ADD - What he'd look like at 20th with Barb4/Fighter16 variant human with 8 feats total and a starting point buy of 13 Str, 15 Dex, 15 Con, 8 Int, 12 Wis, 8 Cha. 4 Feats needed to get DEX and CON maxed
Str 13 Dex 20 Con 20 Int 8 Wis 12 Cha 8
AC: 22 w/shield HP: 269 Move: 40ft
Feats: Mobile, Defensive Duelist, Toughness, plus one for funsies
Give him a rapier(or short sword if you just hate rapiers on barbarians), Archery and Dueling styles, dealing 3 x 1D8+7, crit on 18+, able to almost certainly parry one melee attack per round. Or if you want give him Duel Wielding, plus the Feat, AC 21 still and another attack per round. Going reckless with 4 attks your likely to get 1 crit per round, maybe 2. Dash while raging you can ignore difficult terrain, he'd be pretty darn fierce and solid dishing it out at ranged as well which is often a weak spot for these types of guys. With a little protection magic in ring or shield format he'd have a high enough AC to be able to go reckless often, and with 269hp and resistance to melee it would take quite a bit to drop this guy.