The distinctions here are a bit loose – obviously some of the upper body moves should also engage a bit of your core, but I tried to split them up by main focus.
Upper body
Chin ups
Muscle up
Dips
Push ups (variations: diamond, clap, knee, incline, pike…)
Rows
Archer *
Typewriter *
Core
Hollow hold / dish
L-sit
V-sit
Pike compressions
Knee/leg raises
Toes to bar
Lower body
Squat (variations: pistol, sissy, split, cossack, jump…)
Lunge
Leg extensions
Hamstring curl
Balance
Handstand
Shoulderstand
Full body
Flag
Lever
Elbow lever
Planche
Pullover
Skin the cat