Possible to Have Breast Lift Through Armpit or Transaxillary Incision?

Hi there-
Please be very careful.
It is important to realize that if you wave a bit of money in the air, you will probably be able to find someone to do anything you wish...
As an aside- there is even an eye doctor here in Orlando calling himself a liposuction expert, and an ER doctor who lost his license after he did a "breast lift" by placing a screw used for fixing tendons and bones into a woman's clavicle and pulling the nipple up using a suture tied to the screw (!).
There is no safe and effective way to do what you are suggesting.
The ONLY way to be sure you are always safe and have a high likelihood of achieving your goals is to be sure you are dealing with a surgeon certified by The American Board of Plastic Surgery.
For more advice on how to find a surgeon you like and can trust, please read this:

Lifting the muscles though the armpit will not lift the nipples. Even if this could be done, all it would accomplish is to lift the breast on your chest but do nothing to change the shape. 

The goal of a breast lift is to elevate the nipple-areola so that it is centered on the breast mound. Since the muscles are not connected to the skin, tightening the muscles is not part of a breast lift. There is just no way to avoid removing some skin around the areola in order to do a lift. However, in some cases adding an implant provides a degree of lift without skin removal. This is particularly true if there has been some loss of breast volume after breastfeeding. The question is whether a scar in the armpit will be better than a scar along the edge of the areola, where it is often better in people with darker skin because of the darker pigment of the areola.

No, it is not possible to achieve breast lifting through transaction very incisions.

Breast lifting involves some degree of tightening and lifting the breast skin envelope.  In order to tighten the skin envelope, skin excision is necessary;  this results in the presence of scars. 

Sometimes, the presence of scars is a “dealbreaker”;  patients would prefer to leave their breasts unchanged than to have scars. At other times, patients  prefer to have the improvement in breast position, shape, and (possibly) size  and are willing to accept the trade-off of scars.

I hope this helps.

The question is whether a woman with sagging breasts can get an adequate lift by operating through the armpit and lifting the muscles.  The short answer is not likely.  One can lift the breast slightly by placing implants but if the nipples are pointing down implants alone aren't likely to help.  The situation is one of inadequate breast tissue and/or too much skin.
The first thing to decide is how big you want to be.  If you want to be larger then you'll need some sort of implant.  If you are OK with your size then perhaps one of the many different surgical lifts may be sufficient.  In order to remove excess breast skin, incisions will have to be places on the breast itself.  There really is no way to lift the breast by lifting the muscle.