Also known as the Monkey King, Sun Wukong is a legendary, immortal monkey and MK's mentor. He is actually originally from the classic piece of Chinese fiction, Journey to the West! LEGO Monkie Kid is a sort of sequel to the book, which takes place while he's retired. I've read the book he originates from, of course, but I'm going to mostly focus on his appearance in LEGO Monkie Kid.
Sun Wukong is a confident being, especially in battle, and doesn't shy away from a challenge. Since his retirement, he temporarily became known to laze around, relax and eat (especially peaches and peach chips), not usually stepping in unless he's giving advice, or it concerns MK's (his sucessor's) well-being. However, he still took time to train MK. When he feels like the threat is too great, he has a tendency to run off to take care of the problem himself without telling anyone, in order to try and protect them. This, of course, leads to problems, even if he has good intentions. After the issue was resolved, Sun Wukong took the time to apologize sincerely to MK for causing him trouble. He admits that he never thought he'd be someone's mentor, but he wants to try his best for MK's sake. He's very chatty, and, some would say, like the typical anime protagonist, but that's no mistake; Wukong's original appearance in Journey to the West was what inspired Goku, who, in turn, inspired the typical idea of the male anime protag.
Wukong, as previously stated, is very confident, powerful, but generally relaxed. He's generally optimistic, and, even when he knows things are bad, he tries to pretend it's okay to relax those around him. He has a tendency to refer to those around him as 'bud', and, despite his confident and show-offy nature, he actually has paralyzing stage fright, which is what I believe the kids call 'gap moe'. This, along with his stumbles as MK's mentor, proves that he's powerful, but by no means infallible.
Sun Wukong is a very skilled fighter, and, given that he inspired Goku, he was 'overpowered' before 'overpowered' became a common word. He has great speed, strength, agility and reflexes. He has what is called the 108,000 Leap Somersault, which he uses to dodge enemy's attacks, and he's very proficient with his Golden Staff, and can change its size. He is immortal (in five different ways, including eating a peach of immortality). He also has the power to manipulate yellow Chi energy, generate clouds to ride on, shapeshift, replicate himself, communicate telepathically, and throw fire punches.