Upgrade scenario: Oracle 8.0.5.0.0 to Oracle 12c?
There are multiple solutions to this problem but the driving issues are cost, allowable downtime and complexity.

Golden Gate could be purchased with a one year license and will do a zero downtime upgrade from Oracle 8i to 12. You still have to upgrade from 8.05 to 8i.
Your life could be simplified by using VmWare P2V to convert the machine to a virtual machine without any downtime.  This method allows you to:

get your production database on better hardware which should improve the speed of most operations
allows you to make a copy of the machine, put it on a different subnet and start testing various strategies


I have imported schemas from our Oracle 8i database directly into Oracle 11.2 without issues.  Your mileage may vary depending on character sets, licensed features and any unorthodox strategies your programmers have in the PL/SQL code.

One method that could be easily tested:

buy a new server with some serious hardware like 32GB RAM, install VMWare Esxi
convert your old machine to a virtual
create a development copy of the Oracle 8.05
install another virtual machine with Oracle 12
install another virtual machine with Oracle 10XE or 11XE
take snapshots of all the machines with no changes
take an export of the 8.05 development, import into Oracle 10XE or 11XE, test and verify
data pump to the 12 database
verify the data on 12 and offline the 8.05 and oracle 10XE or 11XE

This method needs downtime. A weekend should be more than adequate and only costs you a new server, Oracle 12 licence and some VMWare software licenses.  Keep in mind that testing and verification can take more time than importing the data.