There are lots of things that can be done to make it faster. If I assume you need to do these UNIONs, then you can speed up the query by :
1. Caching the results, for example,
Can you create an indexed view from the whole statement ? Or there are lots of different WHERE conditions, so there'd be lots of indexed views ? But know that this will slow down modifications (INSERT, etc.) for those tables.
Can you cache it in a different way ? Maybe in the mid layer ?
Can it be recalculated in advance ?
2. Make a covering index. Leading columns are columns form WHERE and then all other columns from the query as included columns
Note that a covering index can be also filtered but filtered index isn't used if the WHERE in the query will have variables / parameters and they can potentially have the value that is not covered by the filtered index (i.e., the row isn't covered)
3. ORDER BY will cause sort
If you can cache it, then it's fine - no sort will be needed (it's cached sorted).
Otherwise, sort is CPU bound (and I/O bound if not in memory). To speed it up, do you use fast collation ? The performance difference between the slowest and fastest collation can be even 3 times. For example, SQL_EBCDIC280_CP1_CS_AS, SQL_Latin1_General_CP1251_CS_AS, SQL_Latin1_General_CP1_CI_AS are one of the fastest collations. However, it's hard to make recommendations if I don't know the collation characteristics you need.
'network packet size' for the connection that does the SELECT should be the maximum value possible - 32,767 bytes if the result set (number of rows) will be big. This can be set on the client side, e.g., if you use .NET and SqlConnection in the connection string. This will minimize CPU overhead when sending data from the SQL Server and will improve performance on both side - client and server. This can boost performance even by tens of percents if the network was the bottleneck.
Use shared memory endpoint if the client is on the SQL Server; otherwise TCP/IP for the best performance.
5. General things
As you said, using isolation level read uncommmitted will improve the performance
Probably you can't do changes beyond rewriting the query, etc. but just in case, adding more memory in case it isn't sufficient now, or using SQL Server 2014 in memory features :-), ... would surely help.
There are way too many things that could be tuned but it's hard to point out the key ones if the question isn't very specific.
Hope this helps a bit