I'm looking for a word that means 'to do or see, etc. something until it no longer fazes you'.
For example, a doctor who is used to seeing blood will not flinch or faint at the sight of it. Usually that 'something' is unpleasant. Acclimatize doesn't quite hit the mark. If memory serves right, the word perhaps begins with an 'i'. Of course, I could be wrong.
Inure — ODO
verb, with object (usually be inured to) Accustom (someone) to something, especially something unpleasant.
"these children have been inured to violence."
"After seven years in the firing line with Rangers and three-and-a-half years prising out body pellets at Goodison Park, Smith is inured to criticism."
See more definitions and examples from OneLook Dictionary Search
In psychology, there is a technical term, which the layman can also use:
desensitize
"desensitization: a behavior modification technique, used especially in treating phobias, in which panic or other undesirable emotional response to a given stimulus is reduced or extinguished, especially by repeated exposure to that stimulus." -- dictionary.com
Note, the therapeutic technique of choice to accomplish this is called Exposure and Response Prevention (ERP).
Usage examples:
As a medical student, you have to desensitize yourself to the sight of blood.
With repeated exposures, you can become less sensitive to the sight of blood.
