In the beginning of this year my DM started a campaign in dnd Beyond and sent the link to us players. I generated my character and she features on his campaign. I access her through my cell phone and all is well. 

I have since generated a profile on dnd Beyond and created a character here for another campaign. My first character is for some reason not visible under my profile, but is still visible under the campaign.  I can still access her through the link from the cell phone, but I am afraid of losing her, if my phone dies. 

Now, how do I tranfer my first character from the first campaign to my profile, so I can access her there?

I presume that by profile you mean account.  If your DM sent you a link and you used it to generate a character, you must have created an account/profile at that time in order to create the character.  Since you created an account after that, you now have two accounts, one for each of the campaigns/characters.  Check and see what account you are logged in to on your phone.  Then you probably need to contact support (the “contact us” link under support below) to merge the accounts.

Another option would be to have your first DM send you an invite link to your new account.  Once you have that in hand, you could unassign your character in the first campaign from your phone, and reclaim it with your new account on another device.  Then log out on your phone and log back in with your newer account to access both characters.