Obtain all medals on the original Ranked Maps in Challenge mode (as Batman)]
Unfortunately, the tricky Challenge mode returns in Arkham Origins. Those who platinumed Arkham City will be pleased to know however that these are considerably easier than the ones from previous games, so if you had no problem with those, you should have no problem with these either. They can be a bit hard to tackle for those who haven't done challenge maps before. They are split into combat and predator. In combat, you need to get a fixed number of points while in Predator you need to do certain tasks to gain medals. These are further split into normal versions and extreme challenges. The normal ones will all be unlocked by the end of the story, while to unlock the extreme challenges you need to complete the first four campaigns (See Olympian), or are unlocked through NG+. In extreme variants, enemies are of more powerful variants, of higher numbers and the medal requirements are tougher. You should also note that for the predator challenges you'll need upgrades, the hardest being the Sonic Shock Batarang at Worst Nightmare rank 10. There are 24 maps in total, 12 of each type and 72 medals up for grabs in total.
General tips for the Ranked Maps:

Combat

Hit, jump, repeat. When you get a combo move, jump into a group of enemies and use the bat swarm (X+[]) to gain points. As soon as you get enough charge for the shock gloves, activate them.
Try not to get hit. Jumping continuously can do the trick but sometimes it is necessary to counter too so don't neglect it. If you remain unhit for the entire challenge, you get 7000 points in bonuses (500 for each round and a 5000 bonus for not getting hit in the entire fight). Also, if you don't break the combo during a round you get 1000 bonus points.
For armoured or Titan enemies, you can use a combo takedown (circle+triangle) if you wish, but you will lose potential points from that enemy, and you can gain a lot more from the bat swarm. You will be able to take down these enemies easily with the sonic shock gloves.
The ground takedown (r2+triangle) when an enemy is on the floor can be effective for points if pulled off but is dangerous as it is impossible to counter an enemies strike while in this move, so use it at your own risk. Definitely use it on the last enemy if possible, or the last couple if the rest are stunned or on the floor.
Predator

Take your time. You don't need to do the medals on the first enemies you KO. Some are a lot easier when there are less enemies left, so wait. If you get spotted, swing quickly around the vantage points and wait for them to lose sight of you.
Make full use of detective vision. In some predators, there is an enemy with a jammer, so take him out first (except for one where you need to leave the jammer enemy until last, disrupting the jammer won't negate the medal as long as you keep that enemy standing).
Use PowerPyx's videos. They are an invaluable help for getting all three medals in a fast time, indicating the best spots for some medals. The playlist can be found here: Batman Arkham Origins - Predator Challenges - YouTube
Use your gadgets wisely. The Remote Claw can be used to quickly attach non-armoured enemies to vantage points, the Sonic Shock batarang can be used to lure enemies to where you need them to be, or blown up for an easy knock down.