Updating to CU8 on SQL Server 2012 SP3 with CU2 Our management has decided to install SQL Server 2012 SP3 CU8.
Current running version has SQL Server 2012 SP3 CU2 installed.

This is like jumping 6 CU's ahead.
Currently there are no AG setup.

Question:
Does the 6 CU jump likely to cause any kind of issues?

Could you please guide me to a checklist to install CU's?
Sql Server updates are incremental. As long as the service pack level isn't changing, there is no need to install any intermediate updates.

In your case, SP2 CU2 can be patched directly to SP2 CU8. There is no need - or use - to install CU3 - CU7 before the CU8. Release notes are not cumulative. This means that to see all the changes between CU2 and CU8, you need to read the release notes for CUs 3-8.

Service packs are similar, RTM can be upgraded to the desired SP without installing other SP version(s) before.

Edit: As per the comment, a replication setup needs special steps for update installation. This is documented in Microsoft's support documentation and depends on topology.