I can use BIOS password, but that is always crackable via some hardware means and this is not 100% safe.
All (well most and some might not be known yet ;) ) bios passwords can be circumvented by using a default password. No hardware required. Just physical access is enough.
Is there any way I can setup my Ubuntu PCs authentication (login) username / password system via some cloud / online account.
No, and it would be rather pointless since it would create a false sense of security.
Reason for this is, in case I lose access to my PC I can change my credentials online and therefore disabling access to PC and my data on my HDD.
You are wrong there. If someone has physcial access to your machine they will be able to access your data if it is not encrypted: all they need is a live cd or to enter grub rescue. Both will grant them root access. There is not even any form of password hacking required since these 2 are the general methods for resetting your admin password in case you forgot them.
If you are that worried about your system please use (full disc or /home partition) encryption. This will make all data unreadable and only accesible when you log in with a password. Use a strong password and others will have a hard time getting to your data. Still not impossible (but it would take a long time to decrypt it).
And even full disc encryption is flawed: if someone really really wants your data nothing stops them from asking you to provide your password. 1 knife, 10 fingers. No contest.