First off ...
What other skills are on your tamer?
As in is he or she a mage tamer? EI, Magery, Med along with the taming skills.. or a bard tamer, music, peace/provo/disco?
As for better places to tame... yep there are three better places... one is in Ilsh..one is in the park located in the felucca Wind and one is located in Covetous Level 2 in felucca...
http://uo.stratics.com/database/view.php?db_content=hunters&id=248
If you have not tried it yet.. Lead Taming is a skill you really need to get a handle on...
As you know or have done you have one macro set up for taming... aka Use skill - taming.. push the macro and you get a target cursor..
In Lead Taming you set up a second taming macro..
In the first box (2D client) use skill - taming
In the second box .. Last Target..
After using the first taming macro which markes the critter as the last target you use the second macro and walk in front of the critter.. in this case the Nightmare... just hold the marco down until you get the "you begin to tame" system message and then let go of the macro and keep walking in front of the critter within a couple of tiles..
Next thing you should do is have a suit that has the highest resists in the mares damage...
Have the cure spell and heal spells on a macro to do fast heals and cures while leading the beast (if mage) and if not a mage pots and petals...
Practice the lead taming on smaller critters till you get a hang of how far you need to be and in staying just out of phys contact
One can lead tame mares without first beating them down once one is compfy with healing and curing while doing it... if a mage you can cast Blade Spirits or EVs and just disspell them just before the mare is redline and if a peace bard just bloody peace the bugger....
If your set on using a Uni to beat it down first, just hop back on it when your getting close to snuffing the mare....