Monthly competitions only look at your monthly stats - lifetime/overall stats are considered not at all.
The rules for each competition are laid out on their individual pages:
In the success-rate challenge, players compete to achieve the highest success-rate percentage for puzzles solved vs. puzzles played. Only players who are ranked in the top 50 of that month's high-score challenge are eligible for this contest. (Ties are broken by total accumulated points.)
In the fastest-solver challenge, players compete to achieve the lowest average solving time for all puzzles solved during the competition month. Only players who are ranked in the top 50 of that month's high-score challenge, and who have a solving percentage of 75% or better, are eligible for this contest.