No, you cannot do that.
Actually this ticket will make you troubled- you ticket will shown you are going to Berlin, not to Dublin, even you can prove ANOTHER ticket from Berlin to Dublin. Only if the tickets are 'transfer tickets'联程机票you can do the transfer. Now you may not be allowed to depart at all.
To give an example: if you travel from Dublin (suppose you have a permit to stay in Ireland) by a low cost airline to Berlin (now, let us say you do not have a Schengen visa) and want to transit to fly to Beijing with AirChina (suppose you have a Chinese nationality). This looks OK, right? No actually it is not. Because you do not have a Schengen visa, you will not be allowed to board on the flight from Dublin to Berlin! This is because the low cost airline may land in a DIFFERENT terminal in Berlin airport which make you have to go to another terminal to board AirChina.
But you may argue against me with other experiences. I will say: if you take a Lufthansa from Dublin to Berlin and want to change another lufthansa flight to Beijing (still let us say you do not have a Schengen visa but you have a permit in Ireland and a Chinese passport), then this is OK. Because all the route are run by the SAME company (or at least the same airgroup, luckily AirChina and Lufthansa are in the same airgroup好像是星空联盟还是什么的)!
So I suggest you to double check with the airlines, the embassies and the person who book such ticket for you.