Hello!
I can help you.
I have a positive experience in that process.
I was done a few Joomla websites optimization successfully.
Site speed was increased from 9 to 2-3 sec.
But this process is complicated. Difficult to give prognosis.
I was checked your site from all possible servers at GTMetrix, there is a result:
Canada = 8,6 sec
USA = 10,3 sec
China = 12,0 sec
UK = 7,8 sec
India = 10,7 sec
Australia = 11,4 sec
Brazil = 13,0 sec
My plan is:
1) Making a full backup
2) Optimize images (decrease image sizes)
3) Analyze your html code and fix if it has some bugs.
4) Minimize your CSS files (decrease size)
5) Minimize your JS files (decrease size)
6) Merge your CSS files in to one (this decrease requests)
7) Merge your CSS files in to one (this decrease requests)
8) some another...
p.s. For this exist a special plugin for Joomla, which very useful.
I can't say how many time it will takes, maybe 2-4 days.
I hope that final result can be ~3-4 sec, maybe less...
After making optimization I propose you to use a CDN service, for example CloudFlare, that must increase speed too.
But these is another story :)