On first look it something on component level, on the page where you made screenshot,
in real can be anything...

Current info not enough, I think would be good to see the query debug, and a bit more detailed description what you did

In terms of modules, the RocketTheme menu is somewhat slow and that component needs some performance attention (the dispatch metric would also include any plugins running in the component). Knowing what extensions are in use here would help too. If it's a core component, an idea about the size of the data on the site could help also.

Probably it is that component code and modules are using heavily
--> 1 or more Joomla API function which has/have degraded performance in J3.4 ?

-- we cannot know without running XDEBUG or ZEND Studio on the website, everything else is guessing

Please retest without the roknav menu and report back. That way you can test if @mbabker is correct (fairly sure he is) but then you will be able to see for yourself

I did have a problem with this. What I did was manually:

• turn off mootools scripts
• turn off jquery scripts
• turn off bootrap
• disable chosen.css manually because it still loads anyway
• create template overrides for all components and modules and remove all tooltips
• use echo to stdout or string catentation rather than pushing and popping /<php ?/>
• replace all language string searches with hardcoded text to stop enormous searches (at least 25% improvement in server response time
• remove all whitespace from generated code
• perform compression on scripts and css files with htaccess directives, disable joomla gzip compression
• rewrote windowing software in a javascript routine less than 8KB total for front end that does almost everything mootools, jquery, and bootrap did.
• removed >200 unused css classes and IDs
• replaced 1500 css rules with 100 that do much the same thing.
• added smaller version of jquery to module at end of pages in async and defer mode where it wasnt being used so it would preload for login and registration. Disalbed this module on com_users component
• added same version of jquery to com_user component
• persuaded isp vendor to support fastcgi

In total, this reduced the libraries needed for most pages from 300KB to 4KB, and css from 80KB to 12KB,

from Got time from 8 seconds load for uncached page to 1 second for most of the site. Sadly in overconfidence I deleted the 4KB tablesort script and have to load 100KB of mootools for client-side table-sort from some prehistoric day I fixed that but Joomla dev wasnt interested, so I stupidly didnt keep it.

Oh, that being said, almost all the performance issues could be fixed with template overrides,and the core is much better.And It only took a month to do.

rewrote windowing software in a javascript routine less than 8KB total for front end that does almost everything mootools, jquery, and bootrap did.

@emeyer444 would you share that?