Li'l Murderer will use Scan on itself to reveal its weakness to Lightning to the party, but this is a trap—attacking it with any form of electrical ability causes it to retaliate with powerful electrical attacks of its own. As long as the party avoids using Lightning attacks, the Li'l Murderer can be beaten easily—it will just keep scanning itself while the player attacks it with physical blows.
If the player does not wish to continually deal with the message that comes along with Scan, it is vulnerable to Stop, which will speed things up a bit. It is also possible to rig the team with Reflect and bait the monster into killing itself. The player can also use it as an opportunity to completely heal the party with Pray without fear of retaliation.