Piecemeal restore of entire database - fastest way to roll forward and restore multiple files
The first sequence you wrote is correct:

Restore file1 filegroup1
restore tlog set2 --roll forward to file 2 backup
restore file2 filegroup1
restore tlog set3 
restore file1 filegroup2
restore tlog set4
restore file2 filegroup2
restore tlog set5
restore tail


You have no need to bring online the first file, then the second file, etc as all you want is to restore the whole database in minimal time.

I've just tried the first sequence as I thought it was right and it worked.

I tried then to restore from full backup + all the log files to find out if it was faster and it was. Certainly my database was small enough, just a test database, but you can try to restore your database to another database or to another server in both ways to compare the time.