First thing to note is that you
must start your career in "Kart One" (Tier 8). If you have started in any other discipline, you'll unfortunately have to start a new career otherwise this will not unlock.
As you progress through the career and finish each season, you will receive invitations in your Inbox to either join a new team or renew your contract for the following season. You should be aiming to progress at least 1 tier in each new season (sometimes you can progress more than 1 tier) in order to be able to join a team in the "LMP1" (Tier 1) discipline within ten seasons,
The disciplines are as follows:
Tier 8 - Kart One
Tier 7 - Superkart
Tier 6 - Formula Rookie / Touring (Renault Cup)
Tier 5 - Formula Gulf / GT5
Tier 4 - Formula C / GT4 / Prototype 1
Tier 3 - Formula B / GT3 / Prototype 2
Tier 2 - Formula A / Endurance / LMP2
Tier 1 - LMP1
Note that some disciplines have more than 1 championship associated with them, for example LMP1 has a European, and a World Championship. The European championship acts as a qualifying event for the World Championship, and it is the World Championship that you must win in order to unlock this trophy (and indeed the trophies for "consecutive championships").
To speed things up, you can retire from races where you already have enough points to win the championship, as well as skip events that you have already completed in a previous season - but I would double check this by navigating back to your
Profile -> Career -> Accolades screen. The game should not let you skip any main career-based events that would mess up your progress toward this trophy, but I preferred to err on the side of caution. If you're enjoying the game, keep racing and you'll unlock the "Mailbox Full" trophy in the process (I think I unlocked this during Season 4).
Reducing the difficulty and session length will not affect this trophy, making it relatively simple even for gamers that are not into the genre. However, this will take a while whether you skip events or not, so strap yourself in for the long haul!