Earning the "Straying" title does not involve beating the boss before the time goddess interferes -- instead, you must let the time goddess save you four times in total. The first time is when you fail initially and the time goddess reveals herself to make the pact, the other three times are triggered by letting time run out continuously after the pact has been made. Since this is the tutorial stage of the game, the goddess will save you each time.
After the fourth time, however, she will warn you that this is "your last chance". This is your cue to go win the level with the massive amounts of experience you've probably accumulated, giving you the title.