I recently moved a 2TB database from Linux, Oracle 11.1 to AIX, Oracle 11.2 using impdp with network_link and parallel options. The data was imported in about two hours and the indexes took another 7 hours. There was no downtime but we kept the users off the system while this was happening.
Here is the command I used on the new server:
nohup impdp system/secret NETWORK_LINK=olddb FULL=y PARALLEL=25 &
Then you can run this to see which parallel process is importing which table:
impdp system attach Import> status Import> parallel=30 << this will increase the parallel processes if you want
I had created all the datafiles in the new database and created a db link named olddb beforehand. The servers were on the same local area network and the network was the bottleneck.
You can also read this on my blog.