I'm fairly new to Infinite Crisis, but I learned how to play Gotham Heights on Robin and experimented with many different builds. This is what I've found works very well for him.

First off, Robin is technically a support character, but he can really dish out the pain in late-game. Although, as a support, he is rather squishy. As Robin, you should always be with at least one other ally, and do not engage in an outnumbered fight unless you are on an allied turret point.

Robin does fairly well at defending nodes against melee enemies, but ranged can be tricky. To deal with ranged players, you will want to position Robin at the far end of the node at all times, and change position relative to your opponent. Ranged characters are designed so that their max range is just barely shorter than the diameter of the node, so every time they try to poke you, they will take a turret blast to the face.

Always try to help allies whenever you can. Robin's presence makes a huge difference. He has many abilities that can control the positions of the enemy team. His Q skill is great for knocking enemy players off of your allies when they are trying to escape. This skill is also great to make some distance if you need to escape.

During large fights, such as for the orbital cannon, Robin excels at disrupting and dividing the whole team. By combining his W and Q skills, Robin's kick will pass through all enemy champions. You can use this trick to get into the center of their group. Once there, quickly release his R ultimate, which will knock them all back in different directions. Afterwards, your team can easily single out the spread-apart enemies and pick them off.

From personal experience, Robin has a difficult time fighting against Joker, Flash, and Doomsday (assuming they know what they're doing). If you have a difficult time with any particular champion refer to the optional items list. If Flash or Joker are ruining your day, grab the Entropy Aegis or the Sword of Beowulf, or both. If Doomsday is raining on your parade, grab the Suit of Sorrows. If there is a good mixture of Attack and Power damagers on the enemy team, you can never go wrong with Ra's al Ghul's Robe.

Simply grabbing the right armor won't always be enough. Especially when dealing with Joker, your movements have to be smart. Running in a straight line after Joker is an esy way to get yourself killed. Joker drops AoE as he kites you along, so weaving a lot will give you the best shot at beating him. Your armor should be able to handle any other hits he throws at you if your build counters him correctly. But again, smart movements are key to playing efficiently with Robin. He is very mobile and can easily take advantage of opporunities, and pull out when things start looking hopeless. I typically average about 0~2 deaths per game with Robin with some smart play.

Once you get the four core items for Robin, his damage output becomes very intimidating. With speed and crit, Robin can 1v1 just about any melee class. However, simply because Robin is squishier, these encounters can be fairly close. If you find yourself losing, just slip out of the fight. His Q skills along with the stolen power Flash's Super Speed make this not only possible, but very easy.

Since everyone knows that Robin is support, he is often overlooked in fights between 2+ players. If he is overlooked, Robin has a very easy double, or even triple kill. If you do get targeted, no worries. Pull back to your allies and play more supportive. There's certainly nothing wrong with getting 20+ assists. Heck, your teammates will end up loving you for always having their backs.

Lastly, in the essence of the support class, Arcane Green Lantern's Healing Wave is a great stolen power to have on Robin. It heals all your allies and gives them extra armor. This can turn the tide in larger fights. It can also be used if you have low health and are having a little difficulty escaping from a pursuer (such as Doomsday, Gaslight Catwoman, or Batman).

That's all I have for now. Feedback is appreciated! I know this text block is a bit unorganized, but if this guide helped you, then that's awesome! I'll update this if I discover any flaws in my build, or if I find out something to make this build even better.