The phrase is correct.

Here, "approach" is a noun, "to" is a preposition, and "unlocking" is a gerund which is required after a preposition.

I recommend English Grammar in Use by Raymond Murphy.  The paper copy is reasonably priced and there is a PDF of the 4th edition floating around the net.

Unit 60 Prepositions + -ing

"If a preposition is followed by a verb, the verb ends in -ing."

My approach to unlocking the power of my mind (such as it is!) is to make a pot of coffee and absorb the caffeine.

The 'to' goes with 'approach - and is followed by -ing. Unless it's the approach to the airport/your house/etc.

Grammar books go through all this, but I agree it is a bit of a wade!

I'm going to unlock the power of my mind. And my approach to unlocking it is caffeine. 

(I was thinking how I could get 'approach to unlock' as a sequence of words and I think I could do it like this: I approach the door to unlock it. In other words, I approach the door in order to unlock it)

But, Chris, I'd say that phrase in Spanish rather with an infinitive. I don't know why it is a gerund here. The whole sentence is "Sister Miriam Joseph rescued that integrated approach to unlocking the power of the mind and presented it for many years to her students at Saint Mary s College in South Bend, Indiana". You say "I'm going to sleep" instead of "I'm going to sleeping", for instance.