Credit to MysticWeirdo from IGN FAQs for the assistance in writing this guide.

Backyard:

Mission 1: Block 3 attacks Hold the block button until you get hit 3 times. Grapples do not count. Once completed exit the mission.

Mission 2: Punch/Kick Combo Press X 3 times in succession, Blocked attacks do not count, exit the mission.

Mission 3: Grapple Arts: bring the opponent over to a corner, press B, then Y to Irish Whip him into a corner Wait for him to stand up, punch him, and repeat, exit the mission.

Mission 4: Dash Attacks This mission is a pain in the ass, and the first choke point in the run. Wait for your turbo to get full, line your opponent up in a line, and press RT and X (or A) do this 5 times, and exit the mission

Mission 5: Whacker usage Pick up the weed whacker, hit your opponent with it 3 times (blocked attacks do not count) exit the mission

Trailer Park

Mission 6: More Grapple Arts Easy Mission, grapple your opponent, and mash RT, until complete. exit the mission

Mission 7: Guard Breaks Build up turbo, and press RT + attack button (X or A) once complete, exit mission

Mission 8: Ground Attacks Knock your opponent to the ground, and hit them once, repeat 5 times, and exit the mission.

Mission 9: Attack Counters Build up turbo, and at the start of your opponent's attack press both triggers at the same time. complete, and exit the mission

Mission 10: Jump Attacks Knock opponent down, climb on the picnic table, and press an attack button. If the table is broken, you can use the trailer, complete and exit the mission.

Pool

Mission 11: Super Moves Wait for your turbo meter to fill up (33 seconds) grapple opponent, and press both attack buttons. complete and exit the mission.

Mission 12: Ledge Throws Grapple your opponent near the pool's edge, and press any attack button, repeat once, and exit the mission

Mission 13: Reversals Get grappled by your opponent, and attempt to guess what he will do: Whip (Y Button), Attack 1 (X), Attack 2 (A), or Submission (B) There is no setup for this, you have to get lucky. repeat 3 times, and exit the mission.

Mission 14: Grapple escapes Wait for your turbo meter to fill up, get grappled by your opponent, and press LT+RT, repeat three times, and exit the mission

Mission 15: Win streak Grab the pool skimmer, and spam attack button 2 (A) Each successful hit with the skimmer does 250. You can chain 3 quick attacks in for 250 each, plus 125 for the ground attack, for 875 damage quickly. If your opponent continues to block, walk away from them until they start walking towards you, You should be able to resume this chain. win 5 matches in a row, and exit the mission

Mission 16: Eastern Title Tournament Skip the cutscene at the start, and follow the same pattern from Mission 15. Timing ends at the screen that displays the Eastern Title.