In order to beat a level, you are required to complete the goal number of intervals (3 for Brisk Walking, Running Efficiency, and Speed Endurance, and 5 for Sprint Intervals) at the goal pace or cadence of that level or higher. Because you might change levels during a program, your level is determined by the lowest level out of your 3 (or 5) highest passed intervals. So, if you complete 3 intervals of Running Efficiency, one at Level 4 and two at Level 5 and pass all intervals, you will achieve Level 4.
If you change levels during a program and you completed the first interval at one level, but then moved up levels, you would need to complete the required number of intervals at the higher level in order to beat that level. For example, if you completed one interval of Running Efficiency at Level 1 and then moved up to Level 5, in order to achieve Level 5 you must complete 3 intervals at Level 5, completing a total of 4 intervals.