I know this is an old one but whilst picking off stuff I've missed, I found a quicker way to do this one rather than playing through up to five seasons, in case anyone still needs this one.
When the negotiation period comes round, save the game (for simplicity purposes we'll call this slot 1). Accept the first offer that you get and advance to the next week when it tells you the negotiations have been successful and the game confirms the transfer. Save the game to slot 2 and exit to the top menu (you should briefly get a message about the game saving system data).
Reload slot 1 and accept any other offers you get from any other clubs and repeat the above process - each time you exit to the main menu and the game saves the system data, it's counting the transfer even though you're promptly reloading an old save.
Note that you do, as noted, need to have signed for at least one club from each country, and offers from other countries only appear during the summer transfer window, not the winter one. I couldn't get the game to give me any Spanish clubs at the end of the first season so I saved the game with me at an Italian club them skipped all matches until the end of the second season, upon which I got the offer I needed to complete the achievement. Much quicker than skipping through five seasons in any case.
Also note if you get called up to the international squad then you can't skip those games (as you're probably doing for all the other if you're still going for this achievement by now).