I'd recommend beginning by observing Solomon Grundy's attack patterns. Mostly he will swing his balls #1 and perform a spin with them #2. A universal way of dodging them is running along the outer part of the arena and using evade when needed.
It's also important not to let Solomon catch you, which might happen after he jumps #1. You can react to this by either performing a counter attack, or just evading correctly. Failing to do so will unfortunately cost you quite a lot of energy. Note that Grundy's energy bar in the upper right corner will be depleting over time and from time to time he will regenerate it #2. As you can easily guess, the key to defeating Solomon is block his ability to regenerate health.
In order to put the plan into action, you will have to turn off the three orange generators on the floor #1 using the Explosive Gel. Luckily you don't have to spray it manually, as you can also use the shortcut prompted by the game (left trigger + X) #2.
Regardless of whether you place the gel at the right place or not, you need to detonate it using the same buttons (left trigger + X). If you have placed the gel at the proper place, the generator will be turned off #1, otherwise you will have to try again. Using this tactic, you will have to switch off all three generators #2.
Quickly approach the kneeling Grundy #1 and use the Beat down by rhythmically pressing X to lead out quick hits. That's unfortunately not the end, as Penguin will turn on the machinery once again and the second phase of the fight will begin #2.
This phase doesn't differ much from the last one, through this time Grundy's attacks will be more powerful. Especially keep an eye on his distance attack #1, as it will force you to keep moving even more than before. Occasionally you might also have to destroy some small "enemies" #2 and it's when the ability to quickly throw Batarangs by pressing (not holding!) the left trigger will come in handy.
Just like before, you have to use the Explosive Gel on the generators #1 and afterwards detonate the planted charges. After switching off all of them, approach Solomon and start pressing X for a quick series of attacks #2.
After hitting him with all the attacks in Beat down, the boss should tremble over. Quickly approach him and press X, his time only once #1. Get ready for mashing A during the cutscene #2. Ending this sequence will let you move to the third phase.
This time it's noticeably different, as Solomon will be attacking you while standing still. Above all avoid the shock waves he generates #1, by jumping above them. Also look out for the long distance ball attacks that he performs #2.
The method of weakening the boss changes in this phase as well. Note that the generators keep changing their colours from orange to blue #1. Plant the Explosive Gel when a given generator is orange. The same goes for choosing the moment to detonate the charge #2, as making it in the wrong moment will bring you nothing.
Traditionally, you have to shut down all the generators on the arena, after which a cutscene should start #1. Approach Grundy and start rhythmically pressing X #2 to defeat him, this time for good.