Lego Batman 2: DC Superheroes Walkthrough Part 21 – Unwelcome Guest, Part 1
Detective Work
Head back to the Batcave just outside of town. A longer cutscene runs where it is revealed that Batman has a massive store of Kryptonite. Robin asks why Batman has so much and Batman replies in case Superman turns into a bad guy. The scene cuts to Lex and Joker who are tracking the synthetic Kryptonite. They break into the Bat Cave and are seeking out the store of the precious mineral.
Lex and Joker
Head forward to the boarding platform and get onto the Bat Motorbike. Star firing on Lex until he loses a heart. He will get angry at that point and destroy the Motorbike. Reassemble the destroyed pieces to create a Suit Changer for Batman: the Electricity Suit.
In the Electricity Suit, head back toward the Computer then turn to the left. The bridge will have some of the cave fall on it. This exposes a stretch of live wires that need to be dealt with. Cross with Batman and plug into the socket on the far side of it, drawing the power away from the bridge.
Continue over to the left to find the next socket. Plug Batman into it to reveal the Bat Suit. Change into the suit then use the Sonar Gun on the clear blue pieces nearby to the right. This will reveal a suit changer for Robin: The Acrobat Suit. Have him hop into it then over to the left, where the Joker will blast the rock bridge over. At the foot of where the bridge was you will find a new assembly pieces. It will create a pole socket for Robin. Throw it into the socket and jump over there. Once there, hit the glowing tool box to reveal a handle you can assemble. This will let Batman jump over there as well.
With all that done, have whoever you would like get into the Bat Jet and start firing on the Joker and Lex. Once they lose another heart, they will destroy the plane. Assemble the pieces of it to make a Suit Changer for Batman with the Power Suit. Head back over to the Computer then to the right of it.
On the right-hand side of the Bat-Cave you will find a boulder comes crashing down. It blocks your way forward but note that it has Silver pieces inside. Use the Power Suit's bombs and blast them to clear the path forward. Now head all the way to the end of the platform. There you will see a device with 2 red buttons. Have Batman and Robin jump up onto the switches. This will reveal the Bat Speedboat. Adjust for the odd aim and this will finish out the last of the battle with both Lex and Joker.
The cutscene runs with them getting both Batman and Robin on the run with the use of the Disassembling Ray. They also get into Batman's store of Kryptonite easily (at least the Joker does). As the Batcave is blown to pieces, Joker and Lex get the Kryptonite and leave.