Tony Hawk RIDE

Just so everyone understands, the text of the achievement says "Multiplayer, Local or Online, Challenge Session: Rematch 10 times", which seems to indicate that you have to do this against another person, but you DON'T. You can do this by yourself, offline, by following the steps TuSeMorte indicates. Just play as both players in a challenge session, trying to do the 5 challenges on a given level. This means you have to go through 10 challenges for each "match". Let one player win (by however many points) and at the end of the 10 challenges for that level, just keep selecting "Play Again". Once you do 10 rematches ("Play Again"s), achievement pops.

To be clear, you don't have to play this online against another person. In fact, I'm not sure that it is possible to get this online against someone, regardless of what the achievement name says. I know me and Keytta tried for 2 hours to get it online together, with no luck, but it popped for me alone after I followed the advice above.

Multiplayer, Local or Online, Challenge Session: Rematch 10 times

To set this up go Main Menu>Party Mode
Session Type=Challenge
Level=Venice
Difficulty=Hardcore

I did not do all 10 rematch in one sitting. Keep in mind you have to play one game then after that match select play again and that is the first rematch of that series. For the sake of time do these in one setting each match takes about 6 to 8 minutes. Just Complete part of a challenge with one skater and the rest of the 5 rounds of that match just pump and turn the skater out of bounds.

Some tips for speeding this up are instead of tapping the start button on the board with you to and Ollie to continue, just press on your controller and then A Button for regular foot or press B Button then for goofy foot. After the 11 match start of the 12 this should pop again do not count your first match of the series.