For the ranked achievement types you must win various matches in Ranked Match and level up to a certain rank. To level up you need to accumulate a certain amount of Battle Points online. Here's how much BP you'll need for each achievement:
One Down!: One Win
To The Victor...: 500BP (D+)
Proof Of Your Victory: 1000BP (C)
While you do earn a certain amount of BP for each victory depending on the level of your opponent (50BP against someone of the same rank) you will also lose a good amount of BP as well (40BP against someone of the same rank) so you'll have to be consistently winning in order to get this.
Despite the searching method changing in Street Fighter X Tekken there are still ways to boost this. Usually players online play under the typical 3 rounds 99 seconds format so any other format can help you and your boosting partner match up more easily. Best search settings are:
Rounds to Win: 1
Timer: 30 seconds
While this seems to be the typical way of searching for boosting you may find yourself pairing up with other boosters searching under the same settings! If this is the case try having you and your partner switch your Locale under System Settings from the Xbox Dashboard to a more obscure country to see if you and your partner can pair up like that!
If you need to find a boosting partner please refer to the Achievement Trading Thread here.