Guilty Gear -Strive-

This is done in the "Castle", "Forest", and "Mayship" areas of the "OFFLINE - DOJO - MISSION" mode. The Combo Missions are at the very bottom of each of those areas, noted by the "COMBO - " prefix for the mission names.

For these challenges, I used Sol for the first two (Castle and Forest), and Potemkin for the last one (Mayship) because his is much easier than Sol's Overdrive Combo. Anyone with any fighting game experience should be able to complete the Combo Challenges with ease, but even if you have none, a little bit of practice and mashing (with Potemkin's, anyway) will easily let you complete them.
Edit: Credit to rholliday, they mentioned Ky's combo for the Forest challenge might be easier than Sol. If you're having an issue with the 2nd challenge with Sol, try giving Ky Kiske's combo a shot.

You have to get at least 3 out of 5 attempts during the mission to count as "CLEARED". If you mess up the first 3 combos, reset the mission and try again (or use the last 2 attempt for practice). For Potemkin's Overdrive, it's actually a fairly long duration Overdrive attack, so if you succeed in the first 3 attempt, just walk up and kick the guy on the last 2 attempts to quickly CLEAR the mission.