Purpose of the reduplication in 一步一步地往上爬
What dROOOze wrote is correct.  一步一步 is like step by step in English.  It can be shortened as 一步步，but it will lose the cadence and some effect.
You can probably apply this structure for every measure word, e. g.  一个一个，一升一升，一条一条，etc.
Well, unlike 一个个 or 一个一个,  个个 denotes the sense of every.  E. g.  我们班同学个个学习好 // Every student in our class studies well.