I went about getting almost all other class achievements via the subclass option (Unlocked at level 20 via Cofy's client order). This is recommended because as you level up, your exp hauls increase, which in turn helps your subclass level up faster. If you want though, you can certainly "play it out" as a Braver and still refer to this solution.
Client orders and daily orders will help you on the road to level 30, so do as many as you can. One thing that can speed this up even more is completing the CO or DO with your high level main class (If you have one), then talking to Bhea at the class counter and switching to braver as the main class. Redeem the CO/DO for exp and watch your level shoot straight up. (At level 50+, you can get one SC to level 30 in just hours with a fresh set of DOs ) These orders only look for the character who completed it, not the class, so use it as you see fit. This also applies to weekly missions, so save them for your subclass if possible.
If you run out of orders and still need exp, run through some urgent/advance quests on a high difficulty to bump up the SC a few levels. A bit slower than the above strat, but still useful, especially if you're trying to cram in multiple characters. Hans's orders are also helpful to a degree, especially if your SC is in the early teens. Also, throw up an exp booster while questing to give yourself a hand.
Finally, if you reach level 30 and the achievement doesn't unlock, switch to another class, then change back to Braver. That'll trigger it.