I am not sure if there is a more badass place to get a tattoo than in your armpit.  Maybe directly on the front of the neck.  But that's about it, as far as painful areas in which to get stellar body art.

A tattoo in the armpit will require some pain endurance.  My own experience of being tattooed near and somewhat in the armpit has been interesting.  Leading up to the edge of the pit was very painful with a sharp kind of cutting sensation, but as we got closer to the armpit, the sensation dulled.  I have not had a tattoo placed directly into my armpit, but I suspect that it would be an intense experience.

The skin of the armpit welts very quickly, making highly detailed lines difficult to execute there.  Bright colors will work, but I imagine that there may be multiple sessions needed to really even out all the ink, since the swelling of the skin may make it difficult to know if the tattoo is entirely filled solidly during the first pass.

Because your some of your lymph nodes are located in the armpits, this may be an area you wish to avoid tattooing.  While I have not heard of anyone ever developing cancer directly or indirectly as a result of tattooing, the deposit of tattoo ink into the lymph nodes is currently being researched by the FDA.

I am not a doctor, so I do not have any certifiable authority to pronounce that tattoos are completely safe on all areas of the body.  However, my opinion is that the exposure to tattoo inks is so brief as to not hold the risks associated with long-term exposure to any of the materials found in them.  Also, while processing any wound, materials will pass through your lymph nodes to be expelled from the body.  This is part of the natural process of healing, and as far as I know, tattoo inks do not collect there to stay forever.  They pass from the body except for the parts encased in the skin.  Within this scar tissue, the tattoo ink is inert and does not interact with the rest of the body's systems.  My thought is that if the tattoo ink is deposited within the skin at the proper depth, there is no need to fear adverse consequences other than perhaps tattoo regret brought on from not thinking your tattoo design through fully, or an allergy to an ingredient in the ink, which you probably would know about before getting tattooed, and therefore would avoid that particular color or product.

Generally, if you are considering getting an armpit tattoo, you probably have a lot of tattoos already and have run out of space - thus filling in even the armpit with beautiful artwork that couldn't fit somewhere else.  Or, you might feel that the armpit is a place where you can hide your tattoo so that nobody will really see it there.

Talk with your tattoo artist to come up with a simple and clear design that will work on this area of skin, and be sure to avoid shaving or waxing your armpit during the healing phase.  With a clear plan, your armpit tattoo can be a beautiful experience rather than a haphazard one.  Good luck!