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He starts the match with 2 chunks to use for armor, walls, his peacemaker, and/or his payload assault. Chunks give him options! Whenever possible, don’t allow him to chunk-up (especially now that he can save his resources with his all-new recycling and more recycling mechanics in S3).
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Use fast, multi-hitting attacks or shadow moves to remove his chunk armor.
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Use grounded heavy normal attacks (such as s.HP/HK and c.HP/HK) and throws to ignore his chunk-armor (please note that these attacks do NOT remove the chunk armor) and set up combos. His chunk-armor doesn’t work in the air either, so don’t be afraid to hit him out of the air or juggle him, if possible. You’ll know when you’ve successfully used a grounded heavy normal to bypass armor due to a bright blue spark and unique sound effect that will appear/be heard upon hit
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Only 2 of Aganos’ attacks hit low - c.HK, a.k.a. the ground stomp (on the 2nd hit) and his c.HP with peacemaker, and only 2 of his (grounded) attacks hit as overhead - close MP and s.HP with peacemaker. This makes him incredibly easy to block. I suggest you block high normally and react to his ground stomp by quickly switching to a low block (you may need to practice this). Alternatively, you can always block low and simply watch for the close MP, s.HP with peacemaker, and the jump-in and neutral jumping attacks.
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His natural disaster and ruin special moves are some of the easiest moves in the game to punish on block - take advantage of it (I recommend using the aformentioned grounded heavy normal attacks or shadow moves, especially against the former, since both options offer long-range attacks against the golem as he bounces off of your block, as well as a way to ignore or remove chunks, respectively).
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His shadow pulverize is easily shadow counterable on block just about anywhere during the move, but don’t do it if he has chunk-armor, as that will give him the advantage.
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You can shadow counter his peacemaker chain combos on block.
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Aganos’ walls can take any combination of 3 “hits” from wall-bounces, ground-bounces, or by knocking Aganos down. The 1st only does damage to the wall it hits, while the latter 2 will do damage to ALL walls that are still standing. Try to incorporate these into a single combo setup, such as doing a wall-bounce ender into a throw (which causes Aganos to hit the wall and then the ground) for quick wall destruction.
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Do not jump so readily when he has walls up, as it can make it easier for him to wall-crash you for massive damage.
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Be ready to tech throws whenever Aganos is anywhere up close, as it’s easier for him to do than other characters AND allows him time to chunk up.
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If Aganos performs shadow payload assault, either interrupt it before he slams into the ground, throw him before the falling rocks hit to reduce damage, or simply block it to reduce most of the damage (you’ll still take chip-damage).
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Aganos can “jump” out of his natural disaster, which can be used as an anti-air or a cross-up.
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If you jump over his natural disaster, he can reverse the direction of his “jump” so be ready to block the potential crossup (reverse your block).
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Be ready to block on wakeup, flip-outs, or combo-breakers to combo-punish any ruins and/or shadow ruins he might throw out, especially if walls are present.
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Don’t use projectiles frequently against Aganos as he can shadow ruin or armor through them, as well as finger-flick them away into nothing.
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Don’t use ANY projectiles while he’s holding a peacemaker, as he can easily throw it to destroy virtually all of them, stagger you, and open you up with a heavy natural disaster for a full-combo punish.
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Reverse block if he jumps over you and attempts to use j.MK (his best ambiguous crossup move).
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His marching stomp (f+HK) is easily shadow-counterable on block (but gets harder when he has more chunks).
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Aganos moves slower in every respect with the more chunks he has stored. Take advantage of the grounded heavy normal attacks mentioned earlier that ignore said chunk-armor, since they’ll be more likely to hit with his slower speed.
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His pulverize and shadow pulverize can hit behind him, but only hits high there, so if you perform a successful crossup and he whiffs your jump-in, duck to avoid the back hits (and maybe block as well if your character has a large hitbox), then punish.
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His shadow pulverize is throw-invulnerable until it hits, so be wary of throwing him on wakeup if he has shadow meter.
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Aganos can “hold” his shadow natural disaster for a short time to catch jump-ins, so be wary of jumping if he has shadow meter, since it also recaptures you on (most) successful hits. Also, during this “hold” the move is projectile invulnerable.
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His shadow ruin is invincible during start-up frames, is projectile invulnerable, and has infinite armor until it hits. This leaves you with very few options when it occurs - you can block it, throw him out of it during startup, or even jump over it in some cases (although that’s incredibly risky).
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Both his close s.HK and c.HK (ground stomp) are shadow-counterable on block, but the former is only shadow-counterable on the 1st hit, since the 2nd hit knocks you back, while the latter is only shadow-counterable when up close (since the 2nd hit is a minor earthquake from a distance).
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Some Aganos players like to use his c.HP to cancel into ruin for an easy wall-crash. If they do this often, you can shadow counter punish the attack on block to counter the ruin. However, if they don’t perform the cancel into ruin, you can whiff, so be careful.
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Some Aganos players like to use his light payload assault to force their opponent to jump in order to “catch” them. Simply block low to avoid this. If they attempt to follow up with a natural disaster jump in the hopes to cross-up, simply block appropriately to whatever may hit you 1st, and then quickly adjust your block accordingly, then punish.
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Some Aganos players like to use multiple pokes, such as with s.LP/LK or c.LP/LK to knock you back, even on block, and position you where they want you for best effect (such as to throw you). You can shadow counter this strategy on block.
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His payload assault (all versions) destroy (most) projectiles.
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His c.HK ground stomp can destroy low projectiles in some situations.
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Many Aganos players like to use a natural disaster or pulverize linker immediately after a successful natural disaster or pulverize opener, respectively, for easy lockouts against players who are hoping to combo-break an AD or manual after the opener. If they do this often, pay attention to what strengths they use for patterns/habits to break appropriately in the future (but also be aware that they can still counter-break you).
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His far s.HP hits high and can be low-profiled by most characters simply by crouching (some larger characters may still have to block).
Well, there you go - 30+ incredibly useful tips to fighting the golem. I’ll add more to this list as I think of them. 
If it wasn’t already obvious, blocking, grounded heavy normals, and shadow counters are your best friends in this matchup. 
Feel free to quote this post wherever needed. 