Ok. I don't think the verb "make (something something)...." is ever really used much with "on..." or "on being (something)...". Probably never. The closest I can think of is "make a bet on"... but that sounds wrong too. That would be phrased "put a bet on (that horse)" or "made a bet that (something would happen)". I'm pretty sure "make....on" is categorically wrong.
I'll give you some additional examples of how to rephrase or even combine the two "She made... effort..." phrases:
"She made a great effort to (study/pass the test)"
"She put in great effort studying (to pass the test)"
"She put great effort into studying to (pass the test)"
I think you can even say "She made a great effort studying (to pass the test)" with no "to" after "effort".
All of these "to" can be thought of as short for "in order to". You could even use "...effort towards..." such as in this example:
"She put great effort towards studying in order to pass the test"
Using "on" doesn't really make sense. You can write a paper on a topic, you can work on a project or goal as in:
"He /worked hard/ on being a good boy."
but effort is something you make in order to do something, or put into/towards some goal.