Shadow Blaziken

If you're lucky enough to have a good Shadow Blaziken, then you've got a gem. This Pokemon has great DPS as a Fire Type, and decent Fighting Type DPS as well. Its one issue is the fact that it is pretty frail, to an even greater degree than basic Blaziken, so you're going to want to dodge a lot if you want to utilize it properly.

Best PvE Offensive Moveset

• Pair Blast Burn* with Fire Spin for outstanding Fire-type DPS.

• Use Blast Burn* + Counter for higher DPS against Ice or/and Steel-types.

• Pair Counter with Focus Blast for a formidable Fighting-type Pokemon.

• Blaze Kick has been nerfed. It's still better than Overheat.

• Overheat is inferior to both new moves and not worth using.

• Brave Bird is underwhelming in every aspect.

• No one actually has Stone Edge. It's also not useful in PvE.

Best PvE Defensive Moveset

• Fire Spin is slightly superior to Counter on defense, hitting more of Shadow Blaziken’s counters for neutral damage. However, Fire Spin also has the issue of sharing a type with Shadow Blaziken's best defensive Charged Move options, leaving it easily walled out when against anything resistant to Fire.

• Blaze Kick hits fast and furious, but it's best paired with Counter to keep different typings.
• Blast Burn has the highest potential damage output of Shadow Blaziken's Charged Moves, but it's also easy to dodge, and is best paired with Counter for the reasons outlined above.
• Brave Bird hits hard, but it lacks relevant counter-coverage and takes a long time to drop. Chances are that Shadow Blaziken will drop long before it's used.
• Stone Edge has a useful typing and is hard to dodge, but Shadow Blaziken will probably drop before it's used.
• Overheat and Focus Blast hit extremely hard, but they're also easy to dodge and yet more moves that Shadow Blaziken will probably only be able to launch once, if at all.

Counter outperforms Fire Spin and also gives Shadow Blaziken some coverage in this moveset. 

What has been anticipated for more than a year has finally arrived, in the form of 2 unique moves. Blast Burn is capable of massive damage for only 50 energy, while Blaze Kick is a mirror copy of the elemental punches and gives Shadow Blaziken some speed by allowing more smooth shield baiting. While this moveset doesn't necessarily help Shadow Blaziken cover its weaknesses, it does let Shadow Blaziken dominate its wins much more cleanly. Brave Bird can be elected for extra coverage, though STAB Blast Burn is more efficient even when resisted. 

A more flexible but very limited moveset that gives Shadow Blaziken some coverage, though depending on the matchups this might not matter as much. If you have the legacy Stone Edge, definitely keep it and unlock Blaze Kick to have this option, but this moveset isn't as significantly different as the previous one. It should be noted that without Blast Burn, Shadow Blaziken can get different results depending on matchups.