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 &
impdp system attach Import> status Import> parallel=30 << this will increase the parallel processes if you want