Solomon Grundy is a rather indirect fight but you need to keep an eye on him. He has an overhead attack that can reach pretty much anywhere. It's fast so you need to dodge as soon as it's coming. His other main attack is that he can spin the chains in a big circle. You have more time to plan this but you need to time your dodge as they balls are going by you.
To defeat him, you must plant explosive gel on the three different pads that keep changing colors and then set them off. You should be prompted to use the quick spray and quick detonate. Notice the little jump Batman does during the quick spray? That actually also counts as a dodge and will work for Solomon's attacks. Just dodge when necessary and plant those explosives. Once all three are destroyed, you can attack Solomon. Go pound on him to start the next phase
Phase 2 is rather similar to the first phase except you need to hit the pads on the ground while they are open and they don't always stay open. You also need to be aware that he might occasionally release a little critter on the ground. This is easily handled with a quick baterang. Go about this fight the same as the last and just remember to be careful to dodge his attacks. When you destroy all three again, pound on him again. Once he's on his back, you need to go up and "Finish Him"
And by that, it means start Phase 3. Phase 3 is similar to Phase 2 except that he hits the ground causing a shockwave that can hit you pretty much anywhere and he does it frequently. You also have to watch out for the little critters because they come at you much faster. Destroy the three pads once more and then attack Solomon Grundy a final time to destroy him.
Phase 4 starts with you being shot at. Just dodge left and right while still making forward progress. Once you are in striking range, let rip on him because he has no defenses. This will be over quickly.