The greatest impediment on the way to an animal portrait is a qualified photo. There's a reason why animal photography is a high profitable form of photography - not few people earning their subsistence from that.

The following tips shall help to shoot rather passable photos of your favorite objects, which then can serve as a good sample for a portrait. 

Meanwhile my tips found enthusiastic fans, among them also a good animal photograph, and have been copied by other internet sites, so I assume that the following tips are really useful.

1. USE A TELE LENS! 
 

In animal photography it is always awkward, if you must approach an animal too close .  A dog, a cat or even a horse will come close up at you then, because they like to have something to eat or they just become curious somehow.  To other, e.g. frantical animals, you can't come close onto normal photo distance so that  only the tele lens can be considered anyway. There also are animals who fear cameras - they can be outflanked that way too.  Animals are much more unceremoniously and natural in their moving and behaving, if you do not stand 2-3 metres before them. Besides, the background becomes blurred more or less what puts the photographed object much more in the centre. It is recommended also for digital photos to use a camera which has a maximized - if possible  OPTICAL -  zoom range.

2. USE A SENSITIVE FILM OR HIGHER ISO-VALUE!

A tele lens "swallows" a lot of light, unless you own expensive equipment.
It is helpful to use a 200 or 400 ASA film or adjust the automatic ISO range on your digital camera to 100-1600, to be able to shoot with shorter shutter speed. Especially for moving animals you need shorter shutter speed. Only a headturn or arm movement can lead to fuzzy pictures

With a 1000-ASA-film (in the meantime also more sensitive films are available) or ISO 1600 - 3200 on your digital camera you can take pictures even inside without photoflash, if enough daylight fills the room. 

Digital pictures can be improved a lot with photo editing programs and failures can be corrected. 
 

3. MAKE A LOT OF PICTURES !

Especially in animal photography it is a MUST to make as much pictures as possible. This was a matter of cost in former times, but today in the era of digital photography do not limitate yourself!

Adjust the camera to "continues pictures" and make a lot of photos even if you thing the animal is not moving and just the same.
 

3. TAKE PICTURES OUTSIDE ! 
 

A photoflash always makes strained colours and even with today's cameras with flash in advance it still comes to unfair reflexes on the eyes of the animals.  Besides animals don't like that glaring light at all. My tomcat always turned his head away, when I arrived with the black camera, because he believed, that it would flash again - he couldn't know, whether I had switched on the photoflash or not. Animals move more natural outside and are much more attentive than at the habitation.

4. DON'T TAKE PICTURES "FROM ABOVE" !

Never take a picture of an animal standing, but sit or lay down respectively put the animal on a table or any other higher point. So you are on the same level with the animal, as it were eye in eye (naturally not very meaningful when regarding horses or other great animals...).
 

5. MAKE THE ANIMAL ATTENTIVE ! 
 

Create a situation in which the animal looks attentive, e.g. maybe fissle with the food box, make noises, etc. With a horse or dog possibly leave the accustomed surrounding (the stable/ court/ garden, the house) and go for a walk. There will be something somewhere that will attract the full attention of the animal - that is the moment to squeeze off!

Contact

I do hope, that these tips will help you. 
Maybe there are some photographic talented people under your friends who will help you. 

And if you are not sure if your photos are qualified enough for a portrait, send them to me for having a look at them: 

or scan them and send them to me by email.(also digital photos possible).
In most cases I can use even photos which are not totally excellent!