What character is that HTML entity?
JavaScript (ES6), 141 122 134 bytes
a=&gt;a.replace(/&amp;([aeiouyAEIOUY](acute|uml)|[aeiouAEIOU](grave|circ)|[aoAO]tilde);/g,b=&gt;b[1]+{g:&quot;̀&quot;,a:&quot;́&quot;,c:&quot;̂&quot;,t:&quot;̃&quot;,u:&quot;̈&quot;}[b[2]])

Followed daavko's example using diacritical marks, and I feel like an idiot for not thinking of using it sooner. Actually gets surprisingly short for JavaScript.
EDIT: Neil caught some bad cases of undefined, which are now fixed.